p-compact group

In mathematics, in particular algebraic topology, a p-compact group is (roughly speaking) a space that is a homotopical version of a compact Lie group, but with all the structure concentrated at a single prime p. This concept was introduced by Dwyer and Wilkerson.[1] Subsequently the name homotopy Lie group has also been used.

Examples

Examples include the p-completion of a compact and connected Lie group, and the Sullivan spheres, i.e. the p-completion of a sphere of dimension

2n − 1,

if n divides p − 1.

Classification

The classification of p-compact groups states that there is a 1-1 correspondence between connected p-compact groups, and root data over the p-adic integers. This is analogous to the classical classification of connected compact Lie groups, with the p-adic integers replacing the rational integers.

gollark: I've not seen it before; looks interesting.
gollark: Not really related: https://esolangs.org/wiki/WHY
gollark: I mean, yes, it *kind of makes a bit of sense*, but it's really unintuitive.
gollark: Oh, that too, seems very stupid.
gollark: This was discussed on the esolangs server a bit back: yes, floats are nice because they're fast and all, but "don't report errors unless explicitly asked for" and "reserve piles of values for nan" seems stupid.

References

Notes
  1. W. G. Dwyer and C. W. Wilkerson, Homotopy fixed-point methods for Lie groups and finite loop spaces, Ann. of Math. (2) 139 (1994), no. 2, 395–442.


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