arXiv math/98010151998-01-06math.GT

A Geometric Characteristic Splitting in all Dimensions

Bernhard Leeb, Peter Scott

备注：: 14 pages
发表信息：: Comm. Math. Helv. 75 (2000), 201-215

英文摘要：

We prove the existence of a geometric characteristic submanifold for non-positively curved manifolds of any dimension greater than or equal to three. In dimension three, our result is a geometric version of the topological characteristic submanifold theorem due to Jaco, Shalen and Johannson.

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。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

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

相关论文

Geometry, Heegaard splittings and rank of the fundamental group of hyperbolic 3-manifolds

In this survey we discuss how geometric methods can be used to study topological properties of 3-manifolds such as their Heegaard genus or the rank of their fundamental group. On the other hand, we also discuss briefly some results relating combinatorial descriptions and geometric properties of hyperbolic 3-manifolds.

2009-04-01math.GT

Geometric Methods In Heegaard Theory

We survey some recent geometric methods for studying Heegaard splittings of 3-manifolds

2020-02-02math.GT

Complexities of 3-manifolds from triangulations, Heegaard splittings, and surgery presentations

We study complexities of 3-manifolds defined from triangulations, Heegaard splittings, and surgery presentations. We show that these complexities are related by linear inequalities, by presenting explicit geometric constructions. We also show that our linear inequalities are asymptotically optimal. Our results are used in [arXiv:1405.1805] to estimate Cheeger-Gromov $L^2$ $ρ$-invariants in terms of geometric group theoretic and knot theoretic data.

2017-08-23math.GT

Detecting geometric splittings in finitely presented groups

We present an algorithm which given a presentation of a group $G$ without 2-torsion, a solution to the word problem with respect to this presentation, and an acylindricity constant $κ$, outputs a collection of tracks in an appropriate presentation complex. We give two applications: the first is an algorithm which decides if $G$ admits an essential free decomposition, the second is an algorithm which; if $G$ is relatively hyperbolic; decides if it admits an essential elementary splitting.

2017-01-09math.GRmath.GT

On splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature

In this paper, we show some splitting theorems for CAT(0) spaces on which a product group acts geometrically and we obtain a splitting theorem for compact geodesic spaces of non-positive curvature. A CAT(0) group $Γ$ is said to be {\it rigid}, if $Γ$ determines the boundary up to homeomorphisms of a CAT(0) space on which $Γ$ acts geometrically. C.Croke and B.Kleiner have constructed a non-rigid CAT(0) group. As an application of the splitting theorems for CAT(0) spaces, we obtain that if $Γ_1$ and $Γ_2$ are rigid CAT(0) groups then so is $Γ_1\times Γ_2$.

2010-05-23math.GRmath.GT

特征2下Khovanov弧代数的一种例外分裂

An Exceptional Splitting of Khovanov's Arc Algebras in Characteristic 2

该研究发现特征2基环下Khovanov弧代数可分解为某结合代数的多项式商代数的同构形式，平面缠结相关双模有对应结论，且整数环上无此类同构。

2022-09-04math.GTmath.QAmath.RT

更多相关论文收起更多论文

Non-isotopic Heegaard splittings of Seifert fibered spaces

We find a geometric invariant of isotopy classes of strongly irreducible Heegaard splittings of toroidal 3-manifolds. Combining this invariant with a theorem of R Weidmann, proved here in the appendix, we show that a closed, totally orientable Seifert fibered space M has infinitely many isotopy classes of Heegaard splittings of the same genus if and only if M has an irreducible, horizontal Heegaard splitting, has a base orbifold of positive genus, and is not a circle bundle. This characterizes precisely which Seifert fibered spaces satisfy the converse of Waldhausen's conjecture.

2009-03-06math.GT

Exponential separation in 4-manifolds

We use a new geometric construction, grope splitting, to give a sharp bound for separation of surfaces in 4-manifolds. We also describe applications of this technique in link-homotopy theory, and to the problem of locating pi_1-null surfaces in 4-manifolds. In our applications to link-homotopy, grope splitting serves as a geometric substitute for the Milnor group.

2000-11-16math.GT

Affine Maps Between CAT(0) Spaces

We study affine maps between CAT(0) spaces with geometric actions, and show that they essentially split as products of dilations and linear maps (on the Euclidean factor). This extends known results from the Riemannian case. Furthermore, we prove a splitting lemma for the Tits boundary of a CAT(0) space with geometric action, a variant of a splitting lemma for geodesically complete CAT(1) spaces by Lytchak.

2014-10-07math.GT

Algebraic and Geometric intersection numbers for free groups

We show that the algebraic intersection number of Scott and Swarup for splittings of free groups coincides with the geometric intersection number for the sphere complex of the connected sum of copies of $S^2\times S^1$.

2008-09-18math.GRmath.GT

Splittings of Non-Finitely Generated Groups

In geometric group theory one uses group actions on spaces to gain information about groups. One natural space to use is the Cayley graph of a group. The Cayley graph arguments that one encounters tend to require local finiteness, and hence finite generation of the group. In this paper, I take the theory of intersections of splittings of finitely generated groups (as developed by Scott, Scott-Swarup, and Niblo-Sageev-Scott-Swarup), and rework it to remove finite generation assumptions. Whereas the aforementioned authors relied on the local finiteness of the Cayley graph, I capitalize on the Ba…

2011-09-13math.GRmath.GT

完全图色同调的一个分裂性质

A splitting property of the chromatic homology of the complete graph

本文引入增强态的组合描述以显式分析色同调，证明了一类图的色同调分裂性质，并计算了完全图的色同调。

2023-07-30math.ATmath.COmath.GT