Homotopy theory of Kac-Moody groups

The homotopy theory of compact Lie groups is very well understood by now. The rich structure of these groups (for example: existence and uniqueness of maximal tori, corresponding Weyl groups etc.) may be exploited to classify these groups. This classification even extends to homotopical versions of these groups known as p-compact groups. In the last few decades a beautiful new class of (non-compact) topological groups has been constructed. These are known as Kac-Moody groups and they share most of the structure that compact Lie groups admit. Kac-Moody groups have been shown to be relevant in mathematical physics and further investigation by several mathematicians (including the speaker) seems to suggest that Kac-Moody groups are surprisingly amenable to homotopical techniques. This makes these groups prime candidates for study from the standpoint of homotopy theory

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