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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A fixed point theorem for manifolds
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by Jan W. Jaworowski PDF
Proc. Amer. Math. Soc. 28 (1971), 275-278 Request permission

Abstract:

A Lefschetz type fixed point theorem is proved extending a recent theorem by Robert F. Brown. It deals with compact maps of the form $f:(M - U,X) \to (M,M - U)$, where $M$ is an $n$-manifold, $X$ is an $(n - 2)$-connected ANR which is closed in $M$ and $U$ is an unbounded component of $M - U$. The map $f$ defines maps $u:M - U \to M - U$ and $v:M \to M$; the Lefschetz numbers of $u$ and $v$ are defined and are shown to be equal; and if this number is nonzero then $f$ has a fixed point.
References
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 275-278
  • MSC: Primary 55.36; Secondary 54.00
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0273604-9
  • MathSciNet review: 0273604