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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fixed points and powers of self-maps of $H$-spaces


Authors: Gregory Lupton and John Oprea
Journal: Proc. Amer. Math. Soc. 124 (1996), 3235-3239
MSC (1991): Primary 55M20, 55P45, 55P62
MathSciNet review: 1328360
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Abstract: We give a new proof of the following result due to Duan: Let $f\,:\, X \to X$ be any self-map of a finite connected $H$-space. Then $f^{k}$ has a fixed point if $k \geq 2$. 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: http://dx.doi.org/10.1090/S0002-9939-96-03405-3
PII: S 0002-9939(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