Abstract
AbstractWe determine the fundamental groups of symmetrizable algebraically simply connected split real Kac-Moody groups endowed with the Kac-Peterson topology. In analogy to the finite-dimensional situation, because of the Iwasawa decomposition G = KAU+, the embedding K ,↪ G is a weak homotopy equivalence, in particular π1(G) = π1(K). It thus suffices to determine π1(K), which we achieve by investigating the fundamental groups of generalized ag varieties. Our results apply in all cases in which the Bruhat decomposition of the generalized ag variety is a CW decomposition- in particular, we cover the complete symmetrizable situation; furthermore, the results concerning only the structure of π1(K) actually also hold in the nonsymmetrizable two-spherical case.
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Algebra and Number Theory
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