The Lefschetz fixed point theorem for noncompact locally connected spaces
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- by R. J. Knill
- Trans. Amer. Math. Soc. 174 (1972), 185-198
- DOI: https://doi.org/10.1090/S0002-9947-1972-0315700-9
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Abstract:
Leray’s notion of convexoid space is localized and used to show that if $f:M \to M$ is a relatively compact map on a locally convex manifold M, and f has no fixed points then its Lefschetz trace is zero. A similar theorem holds for certain adjunction spaces $Y{ \cup _g}Z$ where Y is Q-simplicial and Z is locally convexoid. A number of other properties of locally convexoid spaces are derived; for example, any neighborhood retract of a locally convexoid space is locally convexoid.References
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Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 174 (1972), 185-198
- MSC: Primary 55C20
- DOI: https://doi.org/10.1090/S0002-9947-1972-0315700-9
- MathSciNet review: 0315700