On disk embedding up to s-cobordism

2002/09/20 by Vyacheslav Krushkal, Krushkal, Vyacheslav
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT

paper · pdf · doi:10.48550/arxiv.math/0209273

11 pages, 6 figures

arxiv created 2002/09/20 · openalex publication_date 2002/09/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The disk embedding lemma is a technique underlying the topological classification results in 4-manifold topology for good fundamental groups. The purpose of this paper is to develop new tools for disk embedding that work up to s-cobordism, without restrictions on the fundamental group. As an application we show that a surgery problem gives rise to a collection of capped gropes that fit in the framework of control theory.

Related

• Surfaces in 4-manifolds and the surgery conjecture
• Cores of s-cobordisms of 4-manifolds
• Topological embeddings of disks via configuration categories
• Amenable groups and smooth topology of 4-manifolds
• Codimension 2 embeddings, algebraic surgery and Seifert forms