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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A fixed point theorem for manifolds

Author: Jan W. Jaworowski
Journal: Proc. Amer. Math. Soc. 28 (1971), 275-278
MSC: Primary 55.36; Secondary 54.00
MathSciNet review: 0273604
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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.

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PII: S 0002-9939(1971)0273604-9
Keywords: Manifold, retraction, absolute neighborhood retract, compact map, Lefschetz map, $ \Lambda $-map, fixed point
Article copyright: © Copyright 1971 American Mathematical Society