Surfaces in 4-manifolds and the surgery conjecture
Geometric Topology
2007-05-23 v1
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.
Cite
@article{arxiv.math/0505395,
title = {Surfaces in 4-manifolds and the surgery conjecture},
author = {Vyacheslav Krushkal},
journal= {arXiv preprint arXiv:math/0505395},
year = {2007}
}
Comments
To appear in proceedings of the Fields Institute/McMaster Conference on Geometry and Topology of Manifolds