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Some Homotopy Equivalences for Sporadic Geometries

✍ Scribed by Stephen D Smith; Satoshi Yoshiara

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
466 KB
Volume
192
Category
Article
ISSN
0021-8693

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✦ Synopsis

w

x A previous work RSY90 established the projectivity of the reduced Lefschetz modules of certain sporadic group geometries, and the present paper continues that work in a wider context.

Recent developments in sporadic-group cohomology include some applications w x of RSY90 , which in turn suggested treatment of a broader class of geometries. Recurring similarities in the proofs also led to a more unified treatmentᎏestablishing the stronger result of homotopy equivalence of the p-local geometry with Ž .

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## Abstract By studying the group of self homotopy equivalences of the localization (at a prime __p__ and/or zero) of some aspherical complexes, we show that, contrary to the case when the considered space is a nilpotent, β„°^__m__^ ~#~(__X__~__p__~ ) is in general different from β„°^__m__^ ~#~(__X__)_