Ciprian Manolescu
Given a crossing in a planar diagram of a link in the three-sphere, we show that the knot Floer homologies of the link and its two resolutions at that crossing are related by an exact triangle. As a consequence, we deduce that for any quasi-alternating knot, the total rank of its knot Floer homology is equal to the determinant of the knot.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
An unoriented skein exact triangle in unoriented link Floer homology
本文在无定向链环Floer同调中定义了带映射并证明其构成无定向skein正合三角形，同时通过引入瞬子Floer同调中2-手术正合三角形的Heegaard Floer类比作为关键工具，揭示了无定向纽结Floer同调与$I^{\sharp}$的对应关系。
Skein exact triangles in knot Floer homology
本文为链环Floer同调构造新的skein精确三角族，由有理缠结三元组描述，并建立框架以推广至任意有理缠结三元组。
We show that the bordered-sutured Floer invariant of the complement of a tangle in an arbitrary 3-manifold $Y$, with minimal conditions on the bordered-sutured structure, satisfies an unoriented skein exact triangle. This generalizes a theorem by Manolescu for links in $S^3$. We give a theoretical proof of this result by adapting holomorphic polygon counts to the bordered-sutured setting, and also give a combinatorial description of all maps involved and explicitly compute them. We then show that, for $Y = S^3$, our exact triangle coincides with Manolescu's. Finally, we provide a graded versio…
In an earlier work, we introduced a family of t-modified knot Floer homologies, defined by modifying the construction of knot Floer homology HFK-minus. The resulting groups were then used to define concordance homomorphisms indexed by t in [0,2]. In the present work we elaborate on the special case t=1, and call the corresponding modified knot Floer homology the unoriented knot Floer homology. Using elementary methods (based on grid diagrams and normal forms for surface cobordisms), we show that the resulting concordance homomorphism gives a lower bound for the smooth 4-dimensional crosscap nu…
We study the problem of defining maps on link Floer homology induced by unoriented link cobordisms. We provide a natural notion of link cobordism, disoriented link cobordism, which tracks the motion of index zero and index three critical points. Then we construct a map on unoriented link Floer homology associated to a disoriented link cobordism. Furthermore, we give a comparison with Oszváth-Stipsicz-Szabó's and Manolescu's constructions of link cobordism maps for an unoriented band move.
Spectral sequences in unoriented link Floer homology
本文通过迭代修改的无向skein正合三角形，在二元域上构造了从多种Khovanov同调到多种无向链环Floer同调的谱序列，并给出$S^{3}$中纽结的镜像约化Khovanov同调到纽结Floer同调的谱序列。
We re-derive Manolescu's unoriented skein exact triangle for knot Floer homology over F_2 combinatorially using grid diagrams, and extend it to the case with Z coefficients by sign refinements. Iteration of the triangle gives a cube of resolutions that converges to the knot Floer homology of an oriented link. Finally, we re-establish the homological sigma-thinness of quasi-alternating links.
Real Monopole Floer Homology and Skein Exact Triangles
本文证明了实单极Floer同调的无定向skein正合三角形，并引入了Frøyshov型不变量。
The aim of this paper is to study the skein exact sequence for knot Floer homology. We prove precise graded version of this sequence, and also one using $\HFm$. Moreover, a complete argument is also given purely within the realm of grid diagrams.
In a previous paper, Vértesi and the first author used grid-like Heegaard diagrams to define tangle Floer homology, which associates to a tangle $T$ a differential graded bimodule $\widetilde{\mathrm{CT}} (T)$. If $L$ is obtained by gluing together $T_1, \dotsc, T_m$, then the knot Floer homology $\hat{\mathrm{HFK}}(L)$ of $L$ can be recovered from $\widetilde{\mathrm{CT}} (T_1), \dotsc, \widetilde{\mathrm{CT}} (T_m)$. In the present paper, we prove combinatorially that tangle Floer homology satisfies unoriented and oriented skein relations, generalizing the skein exact triangles for knot Floe…
Unoriented skein exact triangles in equivariant singular instanton Floer theory
本文将等变奇异瞬子Floer理论从纽结扩展到非零行列式链环，证明了无定向辫正合三角形，实现了Murasugi符号行为的范畴化，并揭示了L-space纽结与瞬子范畴化的潜在联系。
We develop a skein exact sequence for knot Floer homology, involving singular knots. This leads to an explicit, algebraic description of knot Floer homology in terms of a braid projection of the knot.
In this paper we develop a braid theoretic approach for computing the Kauffman bracket skein module of the lens spaces $L(p,q)$, KBSM($L(p,q)$), for $q\neq 0$. For doing this, we introduce a new concept, that of an {\it unoriented braid}. Unoriented braids are obtained from standard braids by ignoring the natural top-to-bottom orientation of the strands. We first define the {\it generalized Temperley-Lieb algebra of type B}, $TL_{1, n}$, which is related to the knot theory of the solid torus ST, and we obtain the universal Kauffman bracket type invariant, $V$, for knots and links in ST, via a …
Locally equivalent Floer complexes and unoriented link cobordisms
本文证明塌缩链环 Floer 复形的局部等价类及其 Υ-型不变量是链环配边不变量，并利用这些不变量给出切片亏格和 4 维光滑交叉帽数的下界。
Given any unoriented link diagram, a group of new knot invariants are constructed. Each of them satisfies a generalized 4 term skein relation. The coefficients of each invariant is from a commutative ring. Homomorphisms and representations of such a ring defines new link invariants. In this sense, they produce the well-known Kauffman bracket, the Kauffman 2-variable polynomial, and the $Q$-polynomial.
Non-orientable link cobordisms and torsion order in Floer homologies
本文利用无定向版本的instanton和knot Floer homology，证明了不可定向配边中欧拉示性数与局部极大值数量的不等式，并基于此给出了带解结数和细化配边距离的界限。
We iterate Manolescu's unoriented skein exact triangle in knot Floer homology with coefficients in the field of rational functions over $\mathbb{Z}/2\mathbb{Z}$. The result is a spectral sequence which converges to a stabilized version of delta-graded knot Floer homology. The $(E_2,d_2)$ page of this spectral sequence is an algorithmically computable chain complex expressed in terms of spanning trees, and we show that there are no higher differentials. This gives the first combinatorial spanning tree model for knot Floer homology.
Splitting maps in link Floer homology and integer points in permutahedra
本文借助链环 Floer 同调的手术三角形建立并比较 skein 正合序列，用以研究分裂数与分裂映射，并将 $T(n,n)$ 的分裂映射对应于置换多面体整数点。
Involutions, links, and Floer cohomologies
本文为带反转spin^c结构的对合的spin^c 4-流形和有向链环建立了Seiberg--Witten Floer上同调框架，证明Frøyshov型不等式，并应用于无向曲面拓扑及Nielsen实现等问题。
The unoriented band unknotting numbers of torus knots
本文研究环面结的无向带解结数，利用无向纽结 Floer 同调的挠阶证明其与可由环面参数计算的 pinch 数相等。
Floer lasagna modules from link Floer homology
该研究受链环千层面模构造启发，引入弗洛尔千层面模概念，用纽结弗洛尔同调替代Khovanov-Rozansky同调，描述了特定4-流形的该模并计算了若干例子。
Traditionally introduced in terms of advanced topological constructions, many link invariants may also be defined in much simpler terms given their values on a few initial links and a recursive formula on a skein triangle. Then the crucial question to ask is how many initial values are necessary to completely determine such a link invariant. We focus on a specific class of invariants known as nonzero determinant link invariants, defined only for links which do not evaluate to zero on the link determinant. We restate our objective by considering a set $\mathcal{S}$ of links subject to the condi…
In this paper, we explore the interplay between contact structures and sutured monopole Floer homology. First, we study the behavior of contact elements, which were defined by Baldwin and Sivek, under the operation of performing Floer excisions, which was introduced to the context of sutured monopole Floer homology by Kronheimer and Mrowka. We then compute the sutured monopole Floer homology of some special balanced sutured manifolds, using tools closely related to contact geometry. For application, we obtain an exact triangle for the oriented skein relation in monopole theory and derive a con…
We study the maps induced on link Floer homology by elementary decorated link cobordisms. We compute these for births, deaths, stabilizations, and destabilizations, and show that saddle cobordisms can be computed in terms of maps in a decorated skein exact triangle that extends the oriented skein exact triangle in knot Floer homology. In particular, we completely determine the Alexander and Maslov grading shifts. As a corollary, we compute the maps induced by elementary cobordisms between unlinks. We show that these give rise to a $(1+1)$-dimensional TQFT that coincides with the reduced Khovan…
Ozsvath and Szabo recently constructed an algebraically defined invariant of tangles which takes the form of a DA bimodule. This invariant is expected to compute knot Floer homology. The authors have a similar construction for open braids and their plat closures which can be viewed as a filtered DA bimodule over the same algebras. For a closed diagram, this invariant computes the Khovanov homology of the knot or link. We show that forgetting the filtration, our DA bimodules are homotopy equivalent to a suitable version of the Ozsvath- Szabo bimodules. In addition to giving a relationship betwe…
Knot Floer homology of fibered positive links
该研究确定纤维正链的纽弗洛尔同调的马斯洛夫分次次顶项的秩，结合优选交叉构造等方法完成证明，还得到纤维正纽结单值群不动点的界。
Connected sums and directed systems in knot Floer homologies
本文证明了instanton knot Floer homology的基本性质，主要贡献包括推导其连通和公式、有向skein正合三角形，以及提出适用于所有Floer理论的自由有限生成链复形新模型。
Exact triangle and spectral sequence of the equivariant Floer homology of double branched covers
本文研究双分支覆盖的等变Floer同调，证明其满足与经典情形类似的正合三角和谱序列，从而捕捉自然对合的信息。
To each knot $K\subset S^3$ one can associated its knot Floer homology $\hat{HFK}(K)$, a finitely generated bigraded abelian group. In general, the nonzero ranks of these homology groups lie on a finite number of slope one lines with respect to the bigrading. The width of the homology is, in essence, the largest horizontal distance between two such lines. Also, for each diagram $D$ of $K$ there is an associated Turaev surface, and the Turaev genus is the minimum genus of all Turaev surfaces for $K$. We show that the width of knot Floer homology is bounded by Turaev genus plus one. Skein relati…
The purpose of this thesis is to define a "local" version of Ozsváth and Szabó's Heegaard Floer homology $\operatorname{\widehat{HFL}}$ for links in the 3-dimensional sphere, i.e. a Heegaard Floer homology $\operatorname{\widehat{HFT}}$ for tangles in the closed 3-ball. After studying basic properties of $\operatorname{\widehat{HFT}}$ and its decategorified tangle invariant $\nabla_T^s$, we prove a glueing theorem in terms of Zarev's bordered sutured Floer homology, which endows $\operatorname{\widehat{HFT}}$ with an additional glueing structure. For 4-ended tangles, we repackage this glueing …
Khovanov homology offers a nontrivial generalization of Jones polynomial of links in R^3 (and of Kauffman bracket skein module of some 3-manifolds). In this chapter (Chapter X) we define Khovanov homology of links in R^3 and generalize the construction into links in an I-bundle over a surface. We use Viro's approach to construction of Khovanov homology and utilize the fact that one works with unoriented diagrams (unoriented framed links) in which case there is a simple description of Khovanov long exact sequence of homology. Khovanov homology, over the field Q, is a categorification of the Jon…
We study Heegaard Floer homology and various related invariants (such as the $h$-function) for two-component L-space links with linking number zero. For such links, we explicitly describe the relationship between the $h$-function, the Sato-Levine invariant and the Casson invariant. We give a formula for the Heegaard Floer $d$-invariants of integral surgeries on two-component L-space links of linking number zero in terms of the $h$-function, generalizing a formula of Ni and Wu. As a consequence, for such links with unknotted components, we characterize L-space surgery slopes in terms of the $ν^…
Hyperbolic knots with arbitrarily large torsion order in knot Floer homology
本文证明双曲纽结（主要是扭转环面纽结）可实现任意大的两种纽结弗洛尔同调挠率阶，并首次构造出共享同一 Upsilon 挠率函数的无限族双曲纽结。
In [2] Kauffman and Vogel constructed a rigid vertex regular isotopy invariant for unoriented four-valent graphs embedded in three dimensional space. It assigns to each embedded graph G a polynomial, denoted [G], in three variables, A, B and a, satisfying three skein relations, and is defined in terms of a state-sum and the Dubrovnik polynomial for links. In previous work by the author it is proved, in the case B=A^{-1} and a=A, that for a planar graph G we have [G]=2^{c-1}(-A-A^{-1})^v, where c is the number of connected components of G and v is the number of vertices of G. In this paper we w…
Given an involution on a rational homology 3-sphere $Y$ with quotient the $3$-sphere, we prove a formula for the Lefschetz number of the map induced by this involution in the reduced monopole Floer homology. This formula is motivated by a variant of Witten's conjecture relating the Donaldson and Seiberg--Witten invariants of 4-manifolds. A key ingredient is a skein-theoretic argument, making use of an exact triangle in monopole Floer homology, that computes the Lefschetz number in terms of the Murasugi signature of the branch set and the sum of Frøyshov invariants associated to spin structures…
There are a number of homological knot invariants, each satisfying an unoriented skein exact sequence, which can be realized as the limit page of a spectral sequence starting at a version of the Khovanov chain complex. Compositions of elementary 1-handle movie moves induce a morphism of spectral sequences. These morphisms remain unexploited in the literature, perhaps because there is still an open question concerning the naturality of maps induced by general movies. In this paper we focus on the spectral sequences due to Kronheimer-Mrowka from Khovanov homology to instanton knot Floer homology…
Khovanov homology and exotic $4$-manifolds
通过Khovanov-Rozansky gl_2 skein lasagna模区分怪异结迹，首次证明了怪异紧致定向4维流形的存在，并提出了无法通过规范/弗洛尔理论方法恢复的怪异结迹家族。
Real monopoles and a spectral sequence from Khovanov homology
本文定义带基点链环的实单项量Floer同调$\tilde{HMR}$，证明无定向skein正合三角形，验证其欧拉示性数等于Miyazawa不变量，并构造从约化Khovanov同调到该同调的$\mathbb{F}_2$谱序列。
On the nonorientable four-ball genus of torus knots
本文结合对合与无定向纽结 Floer 同调，给出光滑不可定向四球亏格的新下界，并证明其对多族环面纽结精确，同时否定大量环面纽结可界定局部平坦 Möbius 带。
In \cite{4} Kauffman and Vogel constructed a rigid vertex regular isotopy invariant for unoriented four-valent graphs embedded in three dimensional space. It assigns to each embedded graph $G$ a polynomial, denoted $[G]$, in three variables, $A$, $B$ and $a$, satisfies the skein relation: $$ [\psdiag{2}{6}{overcross}]=A [\psdiag{2}{6}{horlines}]+B [\psdiag{2}{6}{verlines}]+[\psdiag{2}{6}{vertex}]$$ and is defined in terms of a state-sum and the Dubrovnik polynomial for links. Using the graphical calculus of \cite{4} it is shown that the polynomial of a planar graph can be calculated recursivel…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。