Algebraic and Geometric Topology 5 (2005), paper no. 70, pages 1719-1732.

Surgery and involutions on 4-manifolds

Vyacheslav S. Krushkal

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

AMS subject classification. Primary: 57N13. Secondary: 57M10, 57M60.

E-print: arXiv:math.GT/0505394

DOI: 10.2140/agt.2005.5.1719

Submitted: 17 May 2005. Accepted: 2 December 2005. Published: 17 December 2005.

Notes on file formats

Vyacheslav S. Krushkal
Department of Mathematics, University of Virginia
Charlottesville, VA 22904, USA
Email: krushkal@virginia.edu

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