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On averaging Lefschetz numbers

Author: U. Kurt Scholz
Journal: Proc. Amer. Math. Soc. 33 (1972), 607-612
MSC: Primary 55C20
MathSciNet review: 0343262
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Abstract: Let (E, p, X) be a regular covering space where E is a connected metric ANR (absolute neighborhood retract) and let $ f:X \to X$ be a map. This paper investigates the relationship between the Lefschetz number of f and those of its lifts, i.e. maps $ f':E \to E$ so that $ pf' = fp$. In particular, it is shown that to a lift $ f':E \to E$ one may associate a class of lifts $ \mathfrak{L}(f')$ with the property that the Lefschetz number of f is equal to the average of the Lefschetz numbers of maps in $ \mathfrak{L}(f')$.

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Keywords: Lefschetz number, regular covering space, fixed point index
Article copyright: © Copyright 1972 American Mathematical Society

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