Year: 2026
Type: preprint
Abstract: Let $G/P$ be a flag manifold with $G$ simple. We determine the rational homotopy groups $π_{\ast }(G/P)\otimes \mathbb{Q}$ and describe the rational cohomology ring $H^{\ast }(G/P;\mathbb{Q})$ solely in terms of the rational homotopy types of $G$ and $P$, respectively. The proof is based on the restrictions of basic Weyl invariants of $G$ to suitable simple factors of $P$, which also address a key nonvanishing issue not settled by earlier approaches of Meier, Shiga-Tezuka, Kotschick, and Terzic.
Source: arXiv (Cornell University)
Author: Duan, Haibao
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214684799