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Transactions of the American Mathematical Society
Journal Article

Systems of Fixed Point Sets

A. D. Elmendorf
Transactions of the American Mathematical Society
Vol. 277, No. 1 (May, 1983), pp. 275-284
Published by: American Mathematical Society
DOI: 10.2307/1999356
https://www.jstor.org/stable/1999356
Page Count: 10

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Topics: Towers, Functors, Mathematical induction, Mathematical theorems, Homeomorphism, Lie groups, Construction engineering, Maps
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Systems of Fixed Point Sets
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Abstract

Let $G$ be a compact Lie group. A canonical method is given for constructing a $G$-space from homotopy theoretic information about its fixed point sets. The construction is a special case of the categorical bar construction. Applications include easy constructions of certain classifying spaces, as well as $G$-Eilenberg-Mac Lane spaces and Postnikov towers.
Transactions of the American Mathematical Society © 1983 American Mathematical Society