Discrete models for the p–local homotopy theory of compact Lie groups and p–compact groups

Broto, Carles¹ ; Levi, Ran² ; Oliver, Bob³

¹ Departament de Matemàtiques, Universitat Autònoma de Barcelona, E–08193 Bellaterra, Spain
² Department of Mathematical Sciences, University of Aberdeen, Meston Building 339, Aberdeen AB24 3UE, UK
³ LAGA, Institut Galilée, Av J-B Clément, 93430 Villetaneuse, France

Geometry & topology, Tome 11 (2007) no. 1, pp. 315-427.

Résumé

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 ${\left(\mathbb{Z}∕p^{\infty }\right)}^r$ by finite $p$–groups—in the same way that classifying spaces of $p$–local finite groups as defined in our paper [The homotopy theory of fusion systems, J. Amer. Math. Soc. 16 (2003) 779–856] are determined by fusion and linking systems over finite $p$–groups. We call these structures “$p$–local compact groups”.

Détail

DOI : 10.2140/gt.2007.11.315

Keywords: classifying space, $p$–completion, fusion, compact Lie groups, $p$–compact groups

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