Surfaces in 4-manifolds and the surgery conjecture

2005/05/18 by Vyacheslav Krushkal, Krushkal, Vyacheslav
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.math/0505395

To appear in proceedings of the Fields Institute/McMaster Conference on Geometry and Topology of Manifolds

arxiv created 2005/05/18 · arxiv updated 2009/12/01

Abstract

We give a survey of geometric approaches to the topological 4-dimensional surgery and 5-dimensional s-cobordism conjectures, with a focus on the study of surfaces in 4-manifolds. The geometric lemma underlying these conjectures is a statement about smooth immersions of disks and of certain 2-complexes, capped gropes, in a 4-manifold. We also mention a reformulation in terms of the A,B-slice problem, and the relation of this question to recent developments in the study of the classical knot concordance group.

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