Volume 5, issue 4 (2005)

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Surgery and involutions on 4–manifolds

Vyacheslav S Krushkal

Algebraic & Geometric Topology 5 (2005) 1719–1732

arXiv: math.GT/0505394

Abstract

We prove that the canonical 4–dimensional surgery problems can be solved after passing to a double cover. This contrasts the long-standing conjecture about the validity of the topological surgery theorem for arbitrary fundamental groups (without passing to a cover). As a corollary, the surgery conjecture is reformulated in terms of the existence of free involutions on a certain class of 4–manifolds. We consider this question and analyze its relation to the A,B–slice problem.

Keywords
4–manifolds, surgery, involutions
Mathematical Subject Classification 2000
Primary: 57N13
Secondary: 57M10, 57M60
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Publication
Received: 17 May 2005
Accepted: 2 December 2005
Published: 17 December 2005
Authors
Vyacheslav S Krushkal
Department of Mathematics
University of Virginia
Charlottesville VA 22904
USA