#### 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