Pin(2)–equivariant KO–theory and intersection forms of spin 4–manifolds

Lin, Jianfeng

doi:10.2140/agt.2015.15.863

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$\mathrm{Pin}(2)$–equivariant KO–theory and intersection forms of spin $4$–manifolds

Jianfeng Lin

Algebraic & Geometric Topology 15 (2015) 863–902

DOI: 10.2140/agt.2015.15.863

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 $\pm Σ (2, 3, 6 k \pm 1)$ . Along the way, we also give an alternative proof of Furuta’s improvement of $\frac{10}{8}$ –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

Volume 15, issue 2 (2015)