Equivalences of Classifying Spaces Completed at the Prime Two
Share this pageBob Oliver
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.
Table of Contents
Table of Contents
Equivalences of Classifying Spaces Completed at the Prime Two
- Contents v6 free
- Introduction 18 free
- Chapter 1. Higher limits over orbit categories 613 free
- Chapter 2. Reduction to simple groups 1724
- Chapter 3. A relative version of Λ-functors 2532
- Chapter 4. Subgroups which contribute to higher limits 3239
- Chapter 5. Alternating groups 4148
- Chapter 6. Groups of Lie type in characteristic two 4451
- Chapter 7. Classical groups of Lie type in odd characteristic 5259
- Chapter 8. Exceptional groups of Lie type in odd characteristic 6370
- Chapter 9. Sporadic groups 8491
- Chapter 10. Computations of lim[sup(1)](Z[sub(G)]) 98105
- Bibliography 100107