Mapping Spaces, Centralizers, and p-Local Finite Groups of Lie Type
Research output: Book/Report › Ph.D. thesis › Research
We study the space of maps from the classifying space of a finite p-group to theBorel construction of a finite group of Lie type G in characteristic p acting on itsbuilding. The first main result is a description of the homology with Fp-coefficients,showing that the mapping space, up to p-completion, is a disjoint union indexedover the group homomorphism up to conjugation of classifying spaces of centralizersof p-subgroups in the underlying group G. We complement this description bydetermining the actual homotopy groups of the mapping space. These resultstranslate to descriptions of the space of maps between a finite p-group and theuncompleted classifying space of the p-local finite group coming from a finite groupof Lie type in characteristic p, providing some of the first results in this uncompletedsetting.
Original language | English |
---|
Publisher | Department of Mathematical Sciences, Faculty of Science, University of Copenhagen |
---|---|
Publication status | Published - 2017 |
ID: 184146618