Title of paper: Discrete models for the $p$-local homotopy theory of
compact Lie groups and $p$-compact groups
Authors: Carles Broto, Ran Levi, Bob Oliver
AMS Classification: Primary 55R35. Secondary 55R40, 57T10
Addresses of authors:
Departament de Matem\`atiques
Universitat Aut\`onoma de Barcelona
E--08193 Bellaterra, Spain
Department of Mathematical Sciences
University of Aberdeen, Meston Building 339
Aberdeen AB24 3UE, U.K.
LAGA, Institut Galil\'ee
Av. J-B Cl\'ement
93430 Villetaneuse, France
E-mail addresses of authors:
broto@mat.uab.es, ran@maths.abdn.ac.uk, bobol@math.univ-paris13.fr
Abstract:
We define and study a certain class of spaces which includes $p$-completed
classifying spaces of compact Lie groups, classifying spaces of $p$-compact
groups, and $p$-completed classifying spaces of certain locally finite
discrete groups. These spaces are determined by fusion and linking systems
over ``discrete $p$-toral groups'' --- extensions of $(\Z/p^\infty)^r$ by
finite $p$-groups --- in the same way that classifying spaces of $p$-local
finite groups as defined in \cite{BLO2} are determined by fusion and
linking systems over finite $p$-groups. We call these structures
``$p$-local compact groups''.