On the Topology of Kac-Moody groups

Nitu Kitchloo

On the Topology of Kac-Moody groups

Algebraic Topology 2013-01-03 v2

Authors: Nitu Kitchloo

Abstract

We study the topology of spaces related to Kac-Moody groups. Given a split Kac-Moody group over the complex numbers, let K denote the unitary form with maximal torus T having normalizer N(T). In this article we study the cohomology of the flag manifold K/T, as a module over the Nil-Hecke ring, as well as the (co)homology of K as a Hopf algebra. In particular, if F is a field of positive characteristic, we show that H_*(K,F) is a finitely generated algebra, and that H^*(K,F) is finitely generated only if K is a compact Lie group . We also study the stable homotopy type of the classifying space BK and show that it is a retract of the classifying space BN(T). We illustrate our results with the example of rank two Kac-Moody groups.

Keywords

Kac-Moody groups flag manifold cohomology Nil-Hecke ring Hopf algebra classifying space stable homotopy type

Cite

@article{arxiv.0810.0851,
  title  = {On the Topology of Kac-Moody groups},
  author = {Nitu Kitchloo},
  journal= {arXiv preprint arXiv:0810.0851},
  year   = {2013}
}

Comments

The presentation and proofs have been streamlined. There is no change in the statements of the results, or the idea of the proof

On the Topology of Kac-Moody groups

Abstract

Keywords

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