Volume 15, issue 2 (2015)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
$\mathrm{Pin}(2)$–equivariant KO–theory and intersection forms of spin $4$–manifolds

Jianfeng Lin

Algebraic & Geometric Topology 15 (2015) 863–902
Abstract

Using the Seiberg–Witten Floer spectrum and Pin(2)–equivariant KO–theory, we prove new Furuta-type inequalities on the intersection forms of spin cobordisms between homology 3–spheres. We then give explicit constrains on the intersection forms of spin 4–manifolds bounded by Brieskorn spheres ± Σ(2,3,6k ± 1). Along the way, we also give an alternative proof of Furuta’s improvement of 10 8 –theorem for closed spin 4–manifolds.

Keywords
Seiberg–Witten theory, $4$–manifold, equivariant KO–theory
Mathematical Subject Classification 2010
Primary: 57R58
Secondary: 57R57
References
Publication
Received: 23 January 2014
Revised: 4 July 2014
Accepted: 3 August 2014
Published: 22 April 2015
Authors
Jianfeng Lin
Department of Mathematics
University of California Los Angeles
405 Hilgard Avenue
Los Angeles, CA 90095-1555
USA