Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] C. H. Dowker, Homology groups of relations, Ann. of Math. (2) 56 (1952), 84–95. MR 0048030
  • [2] R. J. Knill, 𝑄-simplicial spaces, Illinois J. Math. 14 (1970), 40–51. MR 0258017
  • [3] Solomon Lefschetz, Algebraic Topology, American Mathematical Society Colloquium Publications, v. 27, American Mathematical Society, New York, 1942. MR 0007093
  • [4] André Weil, L’intégration dans les groupes topologiques et ses applications, Actual. Sci. Ind., no. 869, Hermann et Cie., Paris, 1940 (French). [This book has been republished by the author at Princeton, N. J., 1941.]. MR 0005741

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55C20, 22C05

Retrieve articles in all journals with MSC: 55C20, 22C05


Additional Information

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