2008/10/05 by Nitu Kitchloo, Kitchloo, Nitu
Mathematics · #54H11 #55P42 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #math.AT #msc:54H11 #msc:55P42
paper · pdf · doi:10.48550/arxiv.0810.0851
The presentation and proofs have been streamlined. There is no change in the statements of the results, or the idea of the proof
openalex publication_date 2008/10/05 · arxiv created 2013/01/01 · arxiv updated 2013/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.