Orientability of fixed point sets

Edmonds, Allan L.

doi:10.1090/S0002-9939-1981-0603614-7

Orientability of fixed point sets
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by Allan L. Edmonds PDF

Proc. Amer. Math. Soc. 82 (1981), 120-124 Request permission

Abstract:

It is proved that the fixed point set of a smooth involution which preserves orientation and a spin structure on a smooth manifold is necessarily orientable. As an application it is proved that a simply connected spin $4$-manifold with nonzero signature admits no involution which acts by multiplication by $- 1$ on its second rational homology group.

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