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Bulletin of the American Mathematical Society

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Homotopy Lie groups


Author: Jesper M. Møller
Journal: Bull. Amer. Math. Soc. 32 (1995), 413-428
MSC: Primary 55R35; Secondary 55P35
DOI: https://doi.org/10.1090/S0273-0979-1995-00613-0
MathSciNet review: 1322786
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Abstract: Homotopy Lie groups, recently invented by W.G. Dwyer and C.W. Wilkerson [13], represent the culmination of a long evolution. The basic philosophy behind the process was formulated almost 25 years ago by Rector [32, 33] in his vision of a homotopy theoretic incarnation of Lie group theory. What was then technically impossible has now become feasible thanks to modern advances such as Miller's proof of the Sullivan conjecture [25] and Lannes's division functors [22]. Today, with Dwyer and Wilkerson's implementation of Rector's vision, the tantalizing classification theorem seems to be within grasp.

Supported by motivating examples and clarifying exercises, this guide quickly leads, without ignoring the context or the proof strategy, from classical finite loop spaces to the important definitions and striking results of this new theory.


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Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1995-00613-0
Keywords: Finite loop space, p-compact group, maximal torus, Weyl group
Article copyright: © Copyright 1995 American Mathematical Society