Equivalences Of Classifying Spaces Completed At The Prime Two

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Equivalences of Classifying Spaces Completed at the Prime Two

Equivalences of Classifying Spaces Completed at the Prime Two
Author :
Publisher : American Mathematical Soc.
Total Pages : 116
Release :
ISBN-10 : 9780821838280
ISBN-13 : 0821838288
Rating : 4/5 (288 Downloads)

Book Synopsis Equivalences of Classifying Spaces Completed at the Prime Two by : Robert Oliver

Download or read book Equivalences of Classifying Spaces Completed at the Prime Two written by Robert Oliver and published by American Mathematical Soc.. This book was released on 2006 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove here the Martino-Priddy conjecture at the prime $2$: the $2$-completions of the classifying spaces of two finite groups $G$ and $G'$ are homotopy equivalent if and only if there is an isomorphism between their Sylow $2$-subgroups which preserves fusion. This is a consequence of a technical algebraic result, which says that for a finite group $G$, the second higher derived functor of the inverse limit vanishes for a certain functor $\mathcal{Z}_G$ on the $2$-subgroup orbit category of $G$. The proof of this result uses the classification theorem for finite simple groups.


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