Algebra Seminar 

27/02/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building
Bob Oliver, Université Paris XIII

$p$-local compact groups

A $p$-local finite group consists of a fusion system — a category which models the fusion (conjugacy) relations in a finite group — together with enough extra structure to determine an associated classifying space. Also, this classifying space has many of the homotopy theoretic properties of the $p$-completed classifying space of a finite group $G$. A $p$-local compact group is a similar structure, but modelled on fusion relations in a compact Lie group or a $p$-compact group. We will describe in more detail the definition and basic properties of $p$-local compact groups, and also their relation with $p$-completed classifying spaces of compact Lie groups, $p$-compact groups, and certain infinite discrete groups. We then discuss some of the open questions which arise in this subject, such as whether there is a natural definition of connected components. All of this is joint work with Carles Broto and Ran Levi.