Open Access

Duan's fixed point theorem: Proof and generalization

Fixed Point Theory and Applications20062006:17563

https://doi.org/10.1155/FPTA/2006/17563

Received: 25 July 2004

Accepted: 21 July 2005

Published: 26 February 2006

Abstract

Let be an H-space of the homotopy type of a connected, finite CW-complex, any map and the th power map. Duan proved that has a fixed point if . We give a new, short and elementary proof of this. We then use rational homotopy to generalize to spaces whose rational cohomology is the tensor product of an exterior algebra on odd dimensional generators with the tensor product of truncated polynomial algebras on even dimensional generators. The role of the power map is played by a -structure as defined by Hemmi-Morisugi-Ooshima. The conclusion is that and each has a fixed point.

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Authors’ Affiliations

(1)
Department of Mathematics, Dartmouth College

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Copyright

© Arkowitz 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.