PhD Defense Isabelle Laude – University of Copenhagen

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PhD Defense Isabelle Laude

Title: Mapping Spaces, Centralizers, and p-Local Finite Groups of Lie Type

We study the space of maps from the classifying space of a finite p-group to the Borel construction of a finite group of Lie type G in characteristic p acting on its building. 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 indexed over the group homomorphism up to conjugation of classifying spaces of centralizers of p-subgroups in the underlying group G. We complement this description by determining the actual homotopy groups of the mapping space. These results translate to descriptions of the space of maps between a finite p-group and the uncompleted classifying space of the p-local finite group coming from a finite group of Lie type in characteristic p, providing some of the first results in this uncompleted setting.

Supervisor: Prof Jesper Grodal, Math, University of Copenhagen

Assessment committee:

Prof. Jesper Michael Møller (Chairman), MATH, University of Copenhagen

Prof. Bob Oliver, University Paris 13

Ass. Prof. Albert Ruiz Cirera, Universitat Autónoma de Barcelona