TY - BOOK
T1 - Mapping Spaces, Centralizers, and p-Local Finite Groups of Lie Type
AU - Laude, Isabelle
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
UR - https://rex.kb.dk/primo-explore/fulldisplay?docid=KGL01010652001&context=L&vid=NUI&search_scope=KGL&tab=default_tab&lang=da_DK
M3 - Ph.D. thesis
BT - Mapping Spaces, Centralizers, and p-Local Finite Groups of Lie Type
PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen
ER -