Fixed points and powers of self-maps of -spaces

Authors:
Gregory Lupton and John Oprea

Journal:
Proc. Amer. Math. Soc. **124** (1996), 3235-3239

MSC (1991):
Primary 55M20, 55P45, 55P62

DOI:
https://doi.org/10.1090/S0002-9939-96-03405-3

MathSciNet review:
1328360

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Abstract | References | Similar Articles | Additional Information

Abstract: We give a new proof of the following result due to Duan: Let be any self-map of a finite connected -space. Then has a fixed point if . Our proof is based on an approach due to Steve Halperin, whereby the Lefschetz number of a self-map is expressed in terms of the eigenvalues of the induced homomorphism of rational homotopy groups. This allows us to give a considerably shorter proof which avoids most of the technicalities of the original proof.

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Additional Information

**Gregory Lupton**

Affiliation:
Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115

Email:
Lupton@math.csuohio.edu

**John Oprea**

Affiliation:
Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115

Email:
Oprea@math.csuohio.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03405-3

Keywords:
Fixed point,
Lefschetz number,
$H$-space,
rational homotopy

Received by editor(s):
October 20, 1994

Received by editor(s) in revised form:
April 3, 1995

Communicated by:
Thomas Goodwillie

Article copyright:
© Copyright 1996
American Mathematical Society