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A congruence for the signature of an embedded manifold


Author: Robert D. Little
Journal: Proc. Amer. Math. Soc. 112 (1991), 587-596
MSC: Primary 57R95; Secondary 55Q50, 55R50, 55S25, 57S17
DOI: https://doi.org/10.1090/S0002-9939-1991-1049846-4
MathSciNet review: 1049846
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {M^{2n}}$ be a smooth, closed, orientable $ 2n$-manifold and suppose that $ K_x^{2n - 2}$ is an orientable submanifold of $ {M^{2n}}$ dual to a cohomology class $ x$. If $ d$ is a positive integer, the signatures of $ K_{dx}^{2n - 2}$ and $ K_x^{2n - 2}$ are related by a numerical congruence. If $ n$ is odd, then any codimension 2 submanifold of $ {\mathbf{C}}{P^n}$ fixed by a diffeomorphism of odd prime order is dual to the generator of the cohomology algebra.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1049846-4
Keywords: Signature, homotopy complex projective space, group actions
Article copyright: © Copyright 1991 American Mathematical Society

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