A fixed point theorem for manifolds

Jaworowski, Jan W.

doi:10.1090/S0002-9939-1971-0273604-9

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.

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