Orientability of fixed point sets

Author:
Allan L. Edmonds

Journal:
Proc. Amer. Math. Soc. **82** (1981), 120-124

MSC:
Primary 57S17; Secondary 55M35, 57S25

MathSciNet review:
603614

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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 -manifold with nonzero signature admits no involution which acts by multiplication by on its second rational homology group.

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DOI:
https://doi.org/10.1090/S0002-9939-1981-0603614-7

Article copyright:
© Copyright 1981
American Mathematical Society