The classification of p-compact groups for p odd

By Kasper K. S. Andersen, Jesper Grodal, Jesper Møller, Antonio Viruel. 2003

92 citations recorded by the source corpus.

A p-compact group, as defined by Dwyer and Wilkerson, is a purely homotopically defined p-local analog of a compact Lie group. It has long been the hope, and later the conjecture, that these objects should have a classification similar to the classification of compact Lie groups. In this paper we finish the proof of this conjecture, for p an odd prime, proving that there is a one-to-one correspondence between connected p-compact groups and finite reflection groups over the p-adic integers. We do this by providing the last, and rather intricate, piece, namely that the exceptional compact Lie groups are uniquely determined as p-compact groups by their Weyl groups seen as finite reflection groups over the p-adic integers. Our approach in fact gives a largely self-contained proof of the entire classification theorem for p odd.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4e413bcf4be04485bc754bd3db6b7bc500897315

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

More Concise Algebraic Topology: Localization, Completion, and Model Categories (2012, background): “A complete classification, analogous to the classification of compact Lie groups, has recently been obtained [5, 4].”