Poincaré series and rational cohomology rings of Kac-Moody groups and their flag manifolds (1301.2647v1)

Published 12 Jan 2013 in math.AT

Abstract: In this paper, we study the rational cohomology rings of indefinite Kac-Moody groups and their flag manifolds. By extracting the information of cohomology from the Poincar\'{e} series, we are able to determine the rational cohomology rings of Kac-Moody groups and their flag manifolds. Since Kac-Moody groups and their flag manifolds are rational formal, we also determine their rational homotopy groups and rational homotopy types.

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