Dr. Julius Grüning
Researcher
Christian-Albrechts-Universität zu Kiel
E-mail: juliusgruening(at)googlemail.com
Project
61At infinity of symmetric spaces
Publications within SPP2026
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 between K and G, implying π1(G)=π1(K). It thus suffices to determine π1(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 π1(K) more generally also holds in the non-symmetrizable two-spherical situation.
| Journal | Transformation Groups |
| Link to preprint version | |
| Link to published version |
Related project(s):
61At infinity of symmetric spaces