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

arXiv Mathematics eprints
 Pub Date:
 May 2005
 DOI:
 10.48550/arXiv.math/0505395
 arXiv:
 arXiv:math/0505395
 Bibcode:
 2005math......5395K
 Keywords:

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