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VOL. 20 | 1992 Homologically Trivial Smooth Involutions on K3 Surfaces

Abstract

We will show that any smooth involution on a K3 surface induces a non-trivial action on its homology. In fact, a closed spin 4-manifold $M$ with $H_1(M; \mathbf{Z}_2) = 0$ and sign $M \ne 0$ will be shown to admit no homologically trivial locally linear involutions. The proof uses only the $G$-signature theorem and the sublattices and branched coverings arguments.

Information

Published: 1 January 1992
First available in Project Euclid: 17 June 2018

zbMATH: 0808.57013
MathSciNet: MR1208316

Digital Object Identifier: 10.2969/aspm/02010365

Rights: Copyright © 1992 Mathematical Society of Japan

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Vol. 20 • 1 January 1992
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