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Proceedings of the American Mathematical Society

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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 $ 4$-manifold with nonzero signature admits no involution which acts by multiplication by $ - 1$ 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