Some homotopy equivalences for sporadic geometries

[摘要] 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 of [RSY90], which in turn suggested treatment of a broader class of geometries. Recurring similarities in the proofs also led to a more unified treatment - establishing the stronger result of homotopy equivalence of the p-local. geometry with the usual elementary poset A(p)(G). One equivalence method proceeds by means of a new ''closed set'' in a standard technique of Quillen. It was further observed that the larger list of simple groups now treated essentially coincides with those of characteristic p-type, suggesting another equivalence method via the poset B-p(G) of radical (or stubborn) p-subgroups. In particular, one finds that these sporadic groups satisfy an analogue of the Borel-Tits theorem - that normalizers of p-groups lie in simplex stabilizers. Still further intriguing coincidences remain to be explained. (C) 1997 Academic Press.

[发布日期] 1997-06-01