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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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On averaging Lefschetz numbers
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by U. Kurt Scholz PDF
Proc. Amer. Math. Soc. 33 (1972), 607-612 Request permission

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 $\mathfrak {L}(f’)$.
References
  • Felix E. Browder, Asymptotic fixed point theorems, Math. Ann. 185 (1970), 38–60. MR 275408, DOI 10.1007/BF01350760
  • Robert F. Brown, The Lefschetz fixed point theorem, Scott, Foresman & Co., Glenview, Ill.-London, 1971. MR 0283793
    • A. Granas, The Hopf-Lefschetz fixed point theorem for noncompact ANR’s, Proc. Conference on Infinite Dimensional Topology, Baton Rouge, La., 1967.
  • Olof Hanner, Some theorems on absolute neighborhood retracts, Ark. Mat. 1 (1951), 389–408. MR 43459, DOI 10.1007/BF02591376
  • P. J. Hilton and S. Wylie, Homology theory: An introduction to algebraic topology, Cambridge University Press, New York, 1960. MR 0115161
  • Heinz Hopf, Über die algebraische Anzahl von Fixpunkten, Math. Z. 29 (1929), no. 1, 493–524 (German). MR 1545024, DOI 10.1007/BF01180550
  • Sze-tsen Hu, Homotopy theory, Pure and Applied Mathematics, Vol. VIII, Academic Press, New York-London, 1959. MR 0106454
  • Bo-ju Jiang, Estimation of the Nielsen numbers, Chinese Math. – Acta 5 (1964), 330–339. MR 0171279
    • D. McCord, The converse of the Lefschetz fixed point theorem for surfaces and higher dimensional manifolds, Doctoral Dissertation, University of Wisconsin, Madison, Wis., 1970. U. K. Scholz, The Nielsen theory on fixed point classes for Palais maps, Doctoral Dissertation, University of California, Los Angeles, Calif., 1970.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 33 (1972), 607-612
  • MSC: Primary 55C20
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0343262-4
  • MathSciNet review: 0343262