Surgery Description of Orientation-Preserving $D_{2p}$-Actions on Compact Orientable 3-Manifolds

关于手术三维流形的纤维性

On the fiberedness of surgery 3-manifolds

研究闭可定向三维流形中沿纽结的Dehn手术，证明除稀疏斜率外，手术所得流形非曲面纤维化。

通过德恩手术得到双曲三维流形的一般性

Genericity of hyperbolic 3-manifolds via Dehn surgery

研究如何描述链环和德恩手术性质，引入计数模型，证明在该模型下随机链环和随机三维流形是双曲的。

Linking numbers in non-orientable 3-manifolds

The construction of integer linking numbers of closed curves in a three-dimensional manifold usually appeals to the orientation of this manifold. We discuss how to avoid it constructing similar homotopy invariants of links in non-orientable manifolds.

Goodman-Fried surgery, Birkhoff section, and R-covered Anosov flows

In this paper, we show that any topologically transitive Anosov flow on a closed three-dimensional manifold with the orientable weak stable and unstable foliations turns into an R-covered one by a Goodman-Fried surgery along periodic points. When a Birkhoff section of the Anosov flow is given, we can choose the periodic points from the boundary of the Birkhoff section.

Irreducible 3-manifolds that cannot be obtained by 0-surgery on a knot

We give two infinite families of examples of closed, orientable, irreducible 3-manifolds $M$ such that $b_1(M)=1$ and $π_1(M)$ has weight 1, but $M$ is not the result of Dehn surgery along a knot in the 3-sphere. This answers a question of Aschenbrenner, Friedl and Wilton, and provides the first examples of irreducible manifolds with $b_1=1$ that are known not to be surgery on a knot in the 3-sphere. One family consists of Seifert fibered 3-manifolds, while each member of the other family is not even homology cobordant to any Seifert fibered 3-manifold. None of our examples are homology cobord…

保持纤维和反转方向的Seifert纤维化3流形的involution

Fiber-preserving and orientation-reversing involutions of Seifert fibered 3-manifolds

研究了Seifert纤维化3流形上保持纤维和反方向的involution，构造了特定类Ψ，并将其与已知的保持方向情况联系起来。

Heegaard Floer手术公式与美容手术

Heegaard Floer Surgery Formula and Cosmetic Surgeries

本文利用Heegaard Floer同调公式，证明了特定结的美容手术系数必须大于1，并且非整数手术不会与原流形同胚。

Dehn surgery, homology and hyperbolic volume

If a closed, orientable hyperbolic 3--manifold M has volume at most 1.22 then H_1(M;Z_p) has dimension at most 2 for every prime p not 2 or 7, and H_1(M;Z_2) and H_1(M;Z_7) have dimension at most 3. The proof combines several deep results about hyperbolic 3--manifolds. The strategy is to compare the volume of a tube about a shortest closed geodesic C in M with the volumes of tubes about short closed geodesics in a sequence of hyperbolic manifolds obtained from M by Dehn surgeries on C.

Exceptional surgery curves in triangulated 3-manifolds

For the purposes of this paper, Dehn surgery along a curve K in a 3-manifold M with slope r is `exceptional' if the resulting 3-manifold M_K(r) is reducible or a solid torus, or the core of the surgery solid torus has finite order in the fundamental group of M_K(r). We show that, providing the exterior of K is irreducible and atoroidal, and the distance between r and the meridian slope is more than one, and a homology condition is satisfied, then there is (up to ambient isotopy) only a finite number of such exceptional surgery curves in a given compact orientable 3-manifold M, with the boundar…

共定向紧致叶面在伪Anosov映射筒Dehn填充中的共定向紧致叶面

Co-orientable taut foliations in Dehn fillings of pseudo-Anosov mapping tori with co-orientation-reversing monodromy

研究了伪Anosov映射筒Dehn填充后可定向紧致叶面的存在性，证明了特定斜率下填充后存在可定向紧致叶面，并给出了相关例子。

Heegaard diagrams and surgery descriptions for twisted face-pairing 3-manifolds

The twisted face-pairing construction of our earlier papers gives an efficient way of generating, mechanically and with little effort, myriads of relatively simple face-pairing descriptions of interesting closed 3-manifolds. The corresponding description in terms of surgery, or Dehn-filling, reveals the twist construction as a carefully organized surgery on a link. In this paper, we work out the relationship between the twisted face-pairing description of closed 3-manifolds and the more common descriptions by surgery and Heegaard diagrams. We show that all Heegaard diagrams have a natural deco…

源自着色三角剖分的 PL 4-流形三分剖分

Trisections of PL 4-manifolds arising from colored triangulations

本文将gem-诱导三分剖分推广至不可定向紧4-流形，并证明特定边界条件下可自然导出闭4-流形的三分剖分，进而通过着色三角剖分给出闭可定向4-流形三分剖分亏格的估计。

Exceptional surgeries in 3-manifolds

Myers shows that every compact, connected, orientable $3$--manifold with no $2$--sphere boundary components contains a hyperbolic knot. We use work of Ikeda with an observation of Adams-Reid to show that every $3$--manifold subject to the above conditions contains a hyperbolic knot which admits a non-trivial non-hyperbolic surgery, a toroidal surgery in particular. We conclude with a question and a conjecture about reducible surgeries.

关于双曲曲面到双曲3-流形的等变嵌入

On equivariant embeddings of hyperbolic surfaces into hyperbolic 3-manifolds

本文研究了闭双曲曲面到闭双曲3-流形的全测地嵌入及其等变版本，特别探讨了可定向曲面上的大反向作用及不可定向曲面上的大作用。

Reshetikhin-Turaev invariants of Seifert 3-manifolds and a rational surgery formula

We calculate the RT-invariants of all oriented Seifert manifolds directly from surgery presentations. We work in the general framework of an arbitrary modular category as in [V. G. Turaev, Quantum invariants of knots and 3--manifolds, de Gruyter Stud. Math. 18, Walter de Gruyter (1994)], and the invariants are expressed in terms of the S- and T-matrices of the modular category. In another direction we derive a rational surgery formula, which states how the RT-invariants behave under rational surgery along framed links in arbitrary closed oriented 3-manifolds with embedded colored ribbon graphs…

Integral Klein bottle surgeries and Heegaard Floer homology

We study which closed, connected, orientable three-manifolds $X$ containing a Klein bottle arise as integral Dehn surgery along a knot in $S^3$. Such $X$ are presentable as a gluing of the twisted $I$-bundle over the Klein bottle to a knot manifold, and we use a variety of Heegaard Floer type invariants to generate surgery obstructions. Suppose that $X$ is $8$-surgery along a genus two knot, and arises by gluing the twisted $I$-bundle over the Klein bottle to an $S^3$ knot complement. We show that $X$ is an L-space, it must be the dihedral manifold $\left(-1; \tfrac{1}{2}, \tfrac{1}{2}, \tfrac…

Exceptional surgeries on knots with exceptional classes

We survey aspects of classical combinatorial sutured manifold theory and show how they can be adapted to study exceptional Dehn fillings and 2-handle additions. As a consequence we show that if a hyperbolic knot $β$ in a compact, orientable, hyperbolic 3-manifold $M$ has the property that winding number and wrapping number are not equal with respect to a non-trivial class in $H_2(M,\boundary M)$, then, with only a few possible exceptions, every 3-manifold $M'$ obtained by Dehn surgery on $β$ with surgery distance $Δ\geq 2$ will be hyperbolic.

Kirby calculus in manifolds with boundary

Suppose there are two framed links in a compact, connected 3-manifold (possibly with boundary, or non-orientable) such that the associated 3-manifolds obtained by surgery are homeomorphic (relative to their common boundary, if there is one.) How are the links related? Kirby's theorem gives the answer when the manifold is S^3, and Fenn and Rourke extended it to the case of any closed orientable 3-manifold, or twisted S^1 cross S^2. The purpose of this note is to give the answer in the general case, using only minor modifications of Kirby's original proof.

三维流形上的新几何结构：手术与广义几何

New geometric structures on 3-manifolds: surgery and generalized geometry

本文通过广义几何中的$B_3$-广义复结构，证明了任意闭可定向三维流形均存在稳定结构（即一般地直到广义微分同胚为余辛结构），从而统一了余辛结构与正规几乎切触结构。

扩展曲面的有限自由作用

Extending finite free actions of surfaces

本文证明了某些闭可定向曲面的保向同胚有限群能自由作用并扩展到三维流形，但无法扩展至柄体。

Surgery diagrams for contact 3-manifolds

In two previous papers, the two first-named authors introduced a notion of contact r-surgery along Legendrian knots in contact 3-manifolds. They also showed how (at least in principle) to convert any contact r-surgery into a sequence of contact plus or minus 1 surgeries, and used this to prove that any (closed) contact 3-manifold can be obtained from the standard contact structure on the 3-sphere by a sequence of such surgeries. In the present paper, we give a shorter proof of that result and a more explicit algorithm for turning a contact r-surgery into plus or minus 1 surgeries. We use this …

Orientation-reversing free actions on handlebodies

We examine free orientation-reversing group actions on orientable handlebodies, and free actions on nonorientable handlebodies. A classification theorem is obtained, giving the equivalence classes and weak equivalence classes of free actions in terms of algebraic invariants that involve Nielsen equivalence. This is applied to describe the sets of free actions in various cases, including a complete classification for many (and conjecturally all) cases above the minimum genus. For abelian groups, the free actions are classified for all genera.

On large orientation-reversing finite group-actions on 3-manifolds and equivariant Heegaard decompositions

We consider finite group-actions on closed, orientable and nonorientable 3-manifolds; such a finite group-action leaves invariant the two handlebodies of a Heegaard splitting of M of some genus g. The maximal possible order of a finite group-action of an orientable or nonorientable handlebody of genus g > 1 is 24(g-1), and in the present paper we characterize the 3-manifolds M and groups G for which the maximal possible order |G| = 24(g-1) is obtained, for some G-invariant Heegaard splitting of genus g > 1. If M is reducible then it is obtained by doubling an action of maximal possible order 2…

具有亏格一Birkhoff截面的Anosov流的例子

Examples of Anosov flows with genus one Birkhoff sections

本研究证明满足特定条件的传递Anosov流存在亏格一Birkhoff截面，为Fried与Ghys的猜想提供证据，并建立了相关手术操作间的对应关系。

Twisted Link Theory

We introduce stable equivalence classes of oriented links in orientable three-manifolds that are orientation $I$-bundles over closed but not necessarily orientable surfaces. We call these twisted links, and show that they subsume the virtual knots introduced by L. Kauffman, and the projective links introduced by Yu. Drobotukhina. We show that these links have unique minimal genus three-manifolds. We use link diagrams to define an extension of the Jones polynomial for these links, and show that this polynomial fails to distinguish two-colorable links over non-orientable surfaces from non-two-co…

沿纽结的唯一手术描述

Unique Surgery Descriptions along Knots

本文证明非平凡纽结存在无穷多r-手术具唯一纽结手术描述，双曲L-空间纽结的无穷多整数斜率手术流形亦然，还构造了具多个不同手术描述的流形族，推广了特征斜率概念。

Smooth structures on non-orientable four-manifolds and free involutions

In this paper, we investigate existence of inequivalent smooth structures on closed smooth non-orientable 4-manifolds building upon results of Akbulut, Cappell-Shaneson, Fintushel-Stern, Gompf, and Stolz. We add to the number of known constructions and provide new examples of exotic manifolds that are obtained as an application of Gluck twists to the standard smooth structure. Inspection of the smooth structure on the oriented 2-covers yields existence results of orientation-reversing exotic free involutions.

Reversing orientation homeomorphisms of surfaces

Let $M$ be a connected compact orientable surface, $f:M\to \mathbb{R}$ be a Morse function, and $h:M\to M$ be a diffeomorphism which preserves $f$ in the sense that $f\circ h = f$. We will show that if $h$ leaves invariant each regular component of each level set of $f$ and reverses its orientation, then $h^2$ is isotopic to the identity map of $M$ via $f$-preserving isotopy. This statement can be regarded as a foliated and a homotopy analogue of a well known observation that every reversing orientation orthogonal isomorphism of a plane has order $2$, i.e. is a mirror symmetry with respect to …

Surgery obstructions on closed manifolds and the Inertia subgroup

The Wall surgery obstruction groups have two interesting geometrically defined subgroups, consisting of the surgery obstructions between closed manifolds, and the inertial elements. We show that the inertia group $I_{n+1}(π,w)$ and the closed manifold subgroup $C_{n+1}(π,w)$ are equal in dimensions $n+1\geq 6$, for any finitely-presented group $π$ and any orientation character $w\colon π\to \cy 2$.

Recent advances on the non-coherent band surgery model for site-specific recombination

Site-specific recombination is an enzymatic process where two sites of precise sequence and orientation along a circle come together, are cleaved, and the ends are recombined. Site-specific recombination on a knotted substrate produces another knot or a two-component link depending on the relative orientation of the sites prior to recombination. Mathematically, site-specific recombination is modeled as coherent (knot to link) or non-coherent (knot to knot) banding. We here survey recent developments in the study of non-coherent bandings on knots and discuss biological implications.

具有指定基本群的奇异不可定向四维流形

Exotic non-orientable four-manifolds with prescribed fundamental group

本文证明具有指数2子群的有限表示群可作为闭光滑不可定向四维流形的基本群，该流形通过Gluck扭结获得奇异光滑结构，其定向2-覆盖微分同胚，且两种结构在添加不同流形后表现出不等价与稳定化特性。

A birationality result for character varieties

Let M be an orientable, cusped hyperbolic 3-manifold of finite volume. We show that the restriction map from a Dehn surgery component in the PSL(2,C)-character variety of M to the character variety of the boundary of M is a birational isomorphism onto its image. This generalises a result by Nathan Dunfield. A key step in our proof is the exactness of Craig Hodgson's volume differential on the eigenvalue variety.

扩展三维环面的纤维化及其在四维流形中的环面手术应用

Extending Fibrations of the $3$-Torus and Applications to Torus Surgery in $4$-Manifolds

研究在特定条件下的四维流形\(W\)和\(W'\)，通过保定向微分同胚\(f\)构造闭定向四维流形\(X\)使其在\(S^1\)上纤维化，给出了环面手术结果及扩展曾特纳工作，证明特定环面手术结果与\(S^1\)乘以透镜空间微分同胚。

The 191 orientable octahedral manifolds

We enumerate all spaces obtained by gluing in pairs the faces of the octahedron in an orientation-reversing fashion. Whenever such a gluing gives rise to non-manifold points, we remove small open neighbourhoods of these points, so we actually deal with three-dimensional manifolds with (possibly empty) boundary. There are 298 combinatorially inequivalent gluing patterns, and we show that they define 191 distinct manifolds, of which 132 are hyperbolic and 59 are not. All the 132 hyperbolic manifolds were already considered in different contexts by other authors, and we provide here their known `…

将交叉帽置换作为奇点纤维化的单调群

Realizing crosscap transpositions as monodromies of singular fibrations

本文研究了4维流形到表面的映射中的一种新奇点类型M-奇点，证明了围绕M-奇点的单调群是非定向表面的交叉帽置换，并介绍了M-纤维化及其与非定向4维流形的关系，最后构造了一个存在M-纤维化但不具有Lefschetz纤维化的闭合非定向4维流形。

Orientation reversal of manifolds

We call a closed, connected, orientable manifold in one of the categories TOP, PL or DIFF chiral if it does not admit an orientation-reversing automorphism and amphicheiral otherwise. Moreover, we call a manifold strongly chiral if it does not admit a self-map of degree -1. We prove that there are strongly chiral, smooth manifolds in every oriented bordism class in every dimension greater than two. We also produce simply-connected, strongly chiral manifolds in every dimension greater than six. For every positive integer k, we exhibit lens spaces with an orientation-reversing self-diffeomorphis…

The Borel/Novikov conjectures and stable diffeomorphisms of 4-manifolds

Two 4-manifolds are stably diffeomorphic if they become diffeomorphic after connected sum with S^2 x S^2's. This paper shows that two closed, orientable, homotopy equivalent, smooth 4-manifolds are stably diffeomorphic, provided a certain map from the second homology of the fundamental group with coefficients in Z/2 to the L-theory of the group is injective. This injectivity is implied by the Borel/Novikov conjecture for torsion-free groups, which is known for many groups. There are also results concerning the homotopy invariance of the Kirby-Siebenmann invariant. The method of proof is to use…

Involutions of 3-dimensional handlebodies

We study the orientation preserving involutions of the orientable 3-dimensional handlebody $H_g$, for any genus $g$. A complete classification of such involutions is given in terms of their fixed points.

Intrinsic Chirality of Graphs in 3-manifolds

The main result of this paper is that for every closed, connected, orientable, irreducible 3-manifold $M$, there is an integer $ n_M$ such that any abstract graph with no automorphism of order 2 which has a 3-connected minor whose genus is more than $n_M$ has no achiral embedding in $M$. By contrast, the paper also proves that for every graph $γ$, there are infinitely many closed, connected, orientable, irreducible 3-manifolds $M$ such that some embedding of $γ$ in $M$ is pointwise fixed by an orientation reversing involution of $M$.

普通与等变Dehn手术数之间的无界间隙

Unbounded Gaps Between Ordinary and Equivariant Dehn Surgery Numbers

该研究证明对每个整数k≥1，存在一对闭定向3维流形与对合使得其普通Dehn手术数为k、等变Dehn手术数为2k，差值无界，还构造了满足DS(Z)<EDS(Z,σ)的无限多互不同胚不可约透镜空间，解答了K3问题列表的相关问题。

RP²×S²的同伦自等价与非定向4维流形的辫子

Homotopy Self-Equivalences of $\mathbb{R}P^2\times S^2$ and a Braid for non-orientable $4$-Manifolds

该研究计算了RP²×S²的基于自同伦等价类群，构造了非定向4维流形的辫子正合序列，确定了Hambleton–Hillman流形的正规1型，还分析了RP²×S²的捏折映射性质。

更多3流形的非特征斜率

Non-characterizing slopes for more 3-manifolds

该文证明任意紧致可定向3流形中，每个同伦类存在无穷多对不同的纽结，其0-手术保向同胚。

具有 3-流形基本群的 4-流形的同伦分类

Homotopy classification of $4$-manifolds with $3$-manifold fundamental group

本文提出了基于群 $π$ 和同态 $w$ 的准则，使得具有相应基本群和定向特征的闭 4-流形可通过二次 2-型进行同伦分类，并在一大类 3-流形群上验证了该准则，推导出无限二面体基本群 4-流形的同胚分类。

正标量曲率度量存在性的覆盖不稳定性

Covering instability for the existence of positive scalar curvature metrics

本文研究非可定向流形上正标量曲率度量的存在性，证明闭非可定向3-流形与其定向二重覆盖在PSC度量存在性上等价，并构造4至7维中定向二重覆盖允许PSC度量但自身不允许的同伦等价类无穷多反例，同时将Schoen-Yau归纳下降方法推广至非可定向情形。

4-流形中表面的cobordism与concordance

Cobordism and Concordance of Surfaces in 4-Manifolds

本文研究了4-流形中表面的cobordism与concordance，通过扩展Sunukjian的方法，利用Pin^-结构，得出了闭合非定向表面在单连通4-流形中在concordance下的分类结果。

关于 Whitehead 链环外部 Euler 类为 0 的 taut 叶状结构的注记

Note on Euler class 0 taut foliation on the Whitehead link exterior

本文研究 Whitehead 链环外部上余可定向 taut 叶状结构的存在性，证明对偶单位 Thurston 球中大多数格点不能实现为 Euler 类，并结合 saddle fillings、指标公式与 Dehn surgery 拓扑阻碍给出一般性研究方法。

$(1,1)$-分解的Goeritz群

The Goeritz groups of $(1,1)$-decompositions

本文定义了闭可定向3-流形中链环的$(g,n)$-分解及其Goeritz群，并计算了所有$(1,1)$-分解的Goeritz群。

Every knot has characterising slopes

Let K be a knot in the 3-sphere. A slope p/q is said to be characterising for K if whenever p/q surgery on K is homeomorphic, via an orientation-preserving homeomorphism, to p/q surgery on another knot K' in the 3-sphere, then K and K' are isotopic. It was an old conjecture of Gordon, proved by Kronheimer, Mrowka, Ozsvath and Szabo, that every slope is characterising for the unknot. In this paper, we show that every knot K has infinitely many characterising slopes, confirming a conjecture of Baker and Motegi. In fact, p/q is characterising for K provided |p| is at most |q| and |q| is sufficien…

Surgeries on periodic links and homology of periodic 3-manifolds

We show that a closed orientable 3-manifold M admits an action of Z_p with fixed point set S^1 iff M can be obtained as the result of surgery on a p-periodic framed link L and Z_p acts freely on the components of L. We prove a similar theorem for free Z_p-actions. As an interesting application, we prove the following, rather unexpected result: for any M as above and for any odd prime p, H_1(M, Z_p)\ne Z_p. We also prove a similar criterion of 2-periodicity for rational homology 3-spheres.

$c_\text{eff}$ 来自手术与模性

$c_{\rm eff}$ from Surgery and Modularity

本文比较了将 $\widehat{Z}$ 不变量扩展至正定管道3-流形的两种方案，发现它们在 Brieskorn 同调球上一般不兼容，并指出其违反了 $c_{\text{eff}}$、Chern-Simons 不变量与非阿贝尔平坦连接间的预期关系。