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- W2982545534 abstract "We 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, the Iwasawa decomposition $G = KAU_+$ provides a weak homotopy equivalence $K hookrightarrow G$, implying $pi_1(G) = pi_1(K)$. It thus suffices to determine $pi_1(K)$ which we achieve by investigating the fundamental groups of generalized flag varieties. Our results apply in all cases in which the Bruhat decomposition of the generalized flag variety is a CW decomposition $-$ in particular, we cover the complete symmetrizable situation; the result concerning the structure of $pi_1(K)$ more generally also holds in the non-symmetrizable two-spherical situation." @default.
- W2982545534 created "2019-11-08" @default.
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- W2982545534 date "2019-05-31" @default.
- W2982545534 modified "2023-09-27" @default.
- W2982545534 title "Fundamental groups of split real Kac-Moody groups and generalized real flag manifolds. With appendices by Tobias Hartnick and Ralf Kohl and by Julius Gruning and Ralf Kohl" @default.
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