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

 

The Lefschetz fixed point theorem for compact groups


Author: Ronald J. Knill
Journal: Proc. Amer. Math. Soc. 66 (1977), 148-152
MSC: Primary 55C20; Secondary 22C05
MathSciNet review: 0454962
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Abstract: It is shown that every compact group G is a Q-simplicial space where Q is any field of characteristic zero. As a consequence it follows that G satisfies a variation of the Lefschetz fixed point theorem.

It has been known for some time that the Lefschetz fixed point theorem applies to a few spaces other than just ANR spaces, especially if some care is taken to use coefficients in certain fields [2]. The case of all compact groups provides a broad class of spaces which may not have local connectivity of any order. It is shown that every compact group G satisfies the Lefschetz fixed point theorem when coefficients for the homology groups are taken in a field of characteristic zero.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0454962-4
PII: S 0002-9939(1977)0454962-4
Keywords: Compact group, Lefschetz fixed point theorem, Q-simplicial spaces
Article copyright: © Copyright 1977 American Mathematical Society