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J. Korean Math. Soc. 2006; 43(6): 1183-1197

Printed November 1, 2006

Copyright © The Korean Mathematical Society.

On spin alternating group actions on spin 4-manifolds

Kazuhiko Kiyono and Ximin Liu

Dalian University of Technology

Abstract

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Let $X$ be a smooth, closed, connected spin 4-manifold with $b_1(X)=0$ and signature $\sigma(X)$. In this paper we use Seiberg-Witten theory to prove that if $X$ admits a spin alternating $A_4$ action, then $b_2^+(X)\geq |\sigma(X)|/8 +3$ under some non-degeneracy conditions.

Keywords: spin 4-manifolds, alternating group actions, Seiberg-Witten theory

MSC numbers: 57R57, 57M60, 57R15

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