The simple connectivity of $B\Sol(q)$
by Andrew Chermak, Bob Oliver, and Sergey Shpectorov
Andrew Chermak
Department of Mathematics
Kansas State University
Manhattan, KS 66502, USA}
chermak@math.ksu.edu
Bob Oliver
LAGA, Institut Galil\'ee
Av. J-B Cl\'ement
93430 Villetaneuse, France
bobol@math.univ-paris13.fr
Sergey Shpectorov
School of Mathematics
University of Birmingham
Edgbaston, Birmingham, B15 2TT, UK
s.shpectorov@bham.ac.uk
Abstract: A $p$-local finite group is an algebraic structure which
includes two categories, a fusion system and a linking system, which mimic
the fusion and linking categories of a finite group over one of its Sylow
subgroups. The $p$-completion of the geometric realization of the linking
system is the classifying space of the finite group. In this paper, we
study the geometric realization, \emph{without} completion, of linking
systems of certain exotic 2-local finite groups whose existence was
predicted by Solomon and Benson, and prove that they are all simply
connected.
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