透镜空间中的Q-基本面

Geometrically incompressible non-orientable closed surfaces in lens spaces

We consider non-orientable closed surfaces of minimum crosscap number in the $(p,q)$-lens space $L(p,q) \cong V_1 \cup_{\partial} V_2$, where $V_1$ and $V_2$ are solid tori. Bredon and Wood gave a formula for calculating the minimum crosscap number. Rubinstein showed that $L(p,q)$ with $p$ even has only one isotopy class of such surfaces, and it is represented by a surface in a standard form, which is constructed from a meridian disk in $V_1$ by performing a finite number of band sum operations in $V_1$ and capping off the resulting boundary circle by a meridian disk of $V_2$. We show that the…

产生透镜空间的结的Dehn手术和结的种类

Dehn surgeries on knots which yield lens spaces and genera of knots

设$K$是三维球面中的双曲纽结。如果$r$ -手术对$K$产生一个透镜空间，那么我们表明，该透镜空间的基本群的顺序是最多$12g-7$，其中$g$是属的$K$。如果我们专门研究属一的病例，将证明用Dehn手术从属一的双曲结中不能获得透镜空间。因此，结合已知的事实，我们有一个属一个结$K$允许Dehn手术产生一个透镜空间，当且仅当$K$是三叶形。

透镜空间与曲面奇点上的实紧接触结构

Real tight contact structures on lens spaces and surface singularities

本文分类了实心环面上的实紧接触结构，证明 $S^3$ 和 $\mathbb{R}P^3$ 上实紧结构唯一，并给出实透镜空间 $L(p,\pm 1)$ 上实紧结构的计数上下界，通过等变接触手术、实开书分解和实代数曲面奇点构造下界实例。

Small genus knots in lens spaces have small bridge number

In a lens space X of order r a knot K representing an element of the fundamental group pi_1 X = Z/rZ of order s <= r contains a connected orientable surface S properly embedded in its exterior X-N(K) such that the boundary of S intersects the meridian of K minimally s times. Assume S has just one boundary component. Let g be the minimal genus of such surfaces for K, and assume s >= 4g-1. Then with respect to the genus one Heegaard splitting of X, K has bridge number at most 1.

The average dual surface of a cohomology class and minimal simplicial decompositions of infinitely many lens spaces

Discrete normal surfaces are normal surfaces whose intersection with each tetrahedron of a triangulation has at most one component. They are also natural Poincaré duals to 1-cocycles with $\ZZ/2\ZZ$-coefficients. For a fixed cohomology class in a simplicial poset the average Euler characteristic of the associated discrete normal surfaces only depends on the $f$-vector of the triangulation. As an application we determine the minimum simplicial poset representations, also known as crystallizations, of lens spaces $L(2k,q),$ where $2k=qr+1.$ Higher dimensional analogs of discrete normal surfaces …

二 genus Goeritz 等价性在 $L(p,1)$ Lens 空间中

Genus two Goeritz equivalence in lens spaces $L(p,1)$

本文研究了 Lens 空间 $L(p,1)$ 中 genus 二 Heegaard 分解的 Goeritz 组对 Heegaard 表面同调的作用，并提供了两个曲线 Goeritz 等价的同调和同伦障碍。

三维流形的分层三角剖分

Layered-triangulations of 3-manifolds

定义了一类3-流形的单顶点三角剖分，即分层三角剖分。首先描述了三维体的分层三角剖分，然后通过Heegaard分裂将分层三角剖分推广到所有三维流形。本文对立体环面和透镜空间的分层三角剖分进行了全面而详细的分析，并对分层三角剖分中的所有法向曲面和几乎法向曲面进行了分类。透镜空间的最小分层三角剖分提供了一个共同的设置，允许嵌入的非定向表面的透镜空间的分类和嵌入的非可定向曲面在每个这样的透镜空间的分类的新的证明，以及一个新的证明的唯一性的Heegaard分裂的透镜空间。构造了Dehn填充的规范三角剖分，即三角化Dehn填充，并将其应用于Dehn填充的Heegaard分裂和有效三角剖分的研究。定义并探讨了三维流形的一种新表示，它是由边界上具有单顶点2-对称三角剖分的两体的特殊分层三角剖分得到的，称为三角Heegaard剖分。复形的1-骨架（L-图）被确定为翻转复形的商，通过考虑亏格g曲面的那些同态扩展到亏格g体的同胚来组织大部分工作。许多问题仍然悬而未决，特别是在有关的L-图，2-对称三角剖分的一个封闭的可定向曲面，最小分层三角剖分的genus-g-bodies，和关系的分层三角剖分叶理。

Non-simply connected symplectic fillings of lens spaces

We prove results exploring the relationship between the fundamental group and the second Betti number of minimal symplectic fillings of lens spaces. These results unify and generalize several disparate facts appearing in the literature. The Fibonacci numbers make a cameo appearance.

Virtual quandle for links in lens spaces

We construct a virtual quandle for links in lens spaces $L(p,q)$, with $q=1$. This invariant has two valuable advantages over an ordinary fundamental quandle for links in lens spaces: the virtual quandle is an essential invariant and the presentation of the virtual quandle can be easily written from the band diagram of a link.

透镜空间中的接触映射类群与有理解结

The contact mapping class group and rational unknots in lens spaces

本文通过单参数凸曲面理论分类透镜空间紧接触结构中的勒让德与横截有理解结，进而确定了标准接触结构的接触映射类群。

关于伪透镜空间的分类

On the classification of fake lens spaces

本文的第一部分给出了维数≥ 5的伪透镜空间的一个分类，它的基本群是N ≥ 2阶的循环群。分类使用和扩展的结果墙和其他人的情况下N = 2和N奇数和结果的作者的本文件的情况下N的幂2。第二部分研究了不同维数的透镜空间的简单结构集之间的悬挂映射。作为应用，我们得到了伪透镜空间挠率不变量的一个归纳几何描述。