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''.