非Simply Connected 3-流形上桥链演算与Kirby演算的等价性

Cobordism范畴的桥接和缠结表示

Bridged Links and Tangle Presentations of Cobordism Categories

我们开发了一个演算的手术数据，称为桥接链接，其中包括除了链接也对球，描述一个手柄附件。与Kirby等人通常的链接演算相反，这个描述只使用了基本的局部移动（即修改和孤立的取消），并且在非单连通和不连通流形上也有效。特别是，它允许我们通过对具有相同边界的任何其他3-流形进行手术来给出3-流形的表示。本文利用平面带状缠结及其组合规则，对2+1维协边范畴的表示进行了Cerf理论推导。作为一个应用程序，我们给出了一个不同的，更自然的证明的Matveev-Polyak介绍的映射类群，并进一步发现系统的手术介绍一般映射环面。我们讨论了一个自然扩张的ReshetikhinTuraev不变的演算桥接链接。不变性如下-类似于纽结不变量-从简单的标识的基本移动与基本范畴关系的不变性或协积分，分别。因此，我们避免了冗长的计算和不自然的Fenn-Rourke减少原来的证明。此外，我们能够从一个弱得多的“模块性”条件开始，这意味着Turaev的条件。概括的介绍，以配边的表面与边界的概述。

不含1-柄的奇异有理椭圆曲面

Exotic rational elliptic surfaces without 1-handles

Harer，Kas和Kirby证明了椭圆曲面$E(1)_{2,3}$的每一个柄分解都需要1-和3-柄。本文利用有理blow-down和Kirby演算构造了一个与$E(1)_{2,3}$具有相同Seiberg-Witten不变量且不含1-和3-句柄的光滑4-流形.我们的流形给出了第一个例子，无论是一个反例的Harer-Kas-Kirby猜想或同胚，但非同胚对单连通闭光滑4-流形具有相同的非零塞伯格-威滕不变量。

A four dimensional hyperbolic link complement in a standard $S^4$

Using techniques from the theory of Kirby calculus we give an explicit construction of a four dimensional hyperbolic link complement in a 4-manifold that is diffeomorphic to the standard 4-sphere.

A four dimensional hyperbolic link complement in a standard $S^2 \times S^2$

Using techniques from the theory of Kirby calculus we give an explicit construction of a four dimensional hyperbolic link complement in a 4-manifold that is diffeomorphic to a standard $S^2 \times S^2$.

Evaluating TQFT invariants from G-crossed braided spherical fusion categories via Kirby diagrams with 3-handles

A family of TQFTs parametrised by G-crossed braided spherical fusion categories has been defined recently as a state sum model and as a Hamiltonian lattice model. Concrete calculations of the resulting manifold invariants are scarce because of the combinatorial complexity of triangulations, if nothing else. Handle decompositions, and in particular Kirby diagrams are known to offer an economic and intuitive description of 4-manifolds. We show that if 3-handles are added to the picture, the state sum model can be conveniently redefined by translating Kirby diagrams into the graphical calculus of…

关于三维流形的框架链环上的圆手术及其图

On Round Surgery on Framed Links and Their Diagrams for 3-manifolds

本文提出三维流形中框架链环上的圆手术方法，建立圆手术图与Dehn手术图的对应，证明Lickorish-Wallace定理的圆手术类比，并建立圆版本Kirby演算，应用于构造标准Kirby图及证明切触叶状结构的存在。

Berge结II的手术描述和体积：关于最小扭曲的五链节的描述

Surgery descriptions and volumes of Berge knots II: Descriptions on the minimally twisted five chain link

使用Kirby演算，我们明确地通过从Berge的R-R描述的十个家庭的结与透镜空间手术的手术描述的最小扭曲的五个链环（MT 5C）。由于MT 5C允许强对合，我们也给出了相应的纠缠描述。

Kirby定理的接触版本

A contact version of Kirby's theorem

本文引入灯笼移动和链移动两类新的接触Kirby移动，结合已知移动，给出完整的接触Kirby移动集，证明两个接触手术图表示接触同胚的接触流形当且仅当它们可通过一系列平面同位素、Legendrian Reidemeister移动、标准取消对的插入或移除、两种标准接触柄滑动、标准灯笼移动和标准链移动相互转换。

Universal Surgery Problems with Trivial Lagrangian

We study the effect of Nielsen moves and their geometric counterparts, handle slides, on good boundary links. A collection of links, universal for 4-dimensional surgery, is shown to admit Seifert surfaces with trivial Lagrangian. They are good boundary links, with Seifert matrices of a more general form than in known constructions of slice links. We show that a certain more restrictive condition on Seifert matrices is sufficient for proving the links are slice. We also give a correction of a Kirby calculus identity in \cite{FK2}, useful for constructing surgery kernels associated to link-slice…

4-manifolds, surgery on loops and geometric realization of Tietze transformations

In the paper \cite{wall_1}, C.T.C. Wall proved that two smooth closed simply connected 4-manifolds which are homeomorphic are in fact stably diffeomorphic. We prove a similar result which states that two smooth closed 4-manifolds satisfying certain properties are stably diffeomorphic if and only if their signatures agree. The manifolds in question are obtained by surgery on loops. The methods we use are modified surgery of Kreck \cite{kreck} and Kirby calculus.

扭曲面配对三维流形的Heegaard图和外科手术描述

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

我们早期论文中的扭曲面配对构造给出了一种有效的方法，可以机械地、毫不费力地生成无数有趣的闭三维流形的相对简单的面配对描述。相应的描述，在外科手术，或Dehn-filling，揭示了扭曲结构作为一个精心组织的外科手术上的链接。本文给出了闭三维流形的扭面对描述与常用的外科手术描述和Heegaard图描述之间的关系。我们表明，所有的Heegaard图有一个自然的分解成子图称为Heegaard圆柱，其中每个都有一个自然的形状由两个正整数的比率。我们的Heegaard图自然产生的扭曲面配对的描述为那些Heegaard圆柱体都有完整的形状。这个特征使我们能够使用Kirby演算和Heegaard理论的标准工具来解决这个问题，即找到哪些封闭的可定向的3-流形具有扭曲的面对描述。