Some Homotopy Equivalences for Sporadic Geometries
Some Homotopy Equivalences for Sporadic Geometries
复制标题
零星几何的一些同伦等价
DOI：
10.1006/jabr.1996.6955
复制
发表时间：
1997
影响因子：
0.9
通讯作者：
Satoshi Yoshiara
中科院分区：
文献类型：
--
作者：
Stephen D. Smith;Satoshi Yoshiara
以前的工作[RSY 90]建立了某些零星群几何的约化Lefschetz模的投影性，本文在更广泛的背景下继续这项工作。
最近的事态发展，零星组上同调包括一些应用[RSY 90]，这反过来又建议治疗更广泛的一类几何形状。在证明中反复出现的相似性也导致了一个更统一的处理--建立p-局部几何与通常的初等偏序集Ap（G）同伦等价的更强结果。一个等价的方法收益通过一个新的“闭集”在一个标准的技术奎伦。进一步观察到，现在处理的简单群的更大列表基本上与特征p-型的那些一致，这表明通过根（或顽固）p-子群的偏序集Bp（G）的另一种等价方法。特别是，人们发现，这些零星的群体满足类似的Borel-Tits定理的正规化的p-群在于单纯形稳定。还有更多有趣的巧合有待解释。
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 thep-local geometry with the usual elementary poset Ap(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 characteristicp-type, suggesting another equivalence method via the poset Bp(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 ofp-groups lie in simplex stabilizers. Still further intriguing coincidences remain to be explained.