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arXiv · 2609.30591

Rational homotopy theory of flag manifolds

Haibao Duan
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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.

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Haibao Duan. 2026-10-01. Rational homotopy theory of flag manifolds. https://arxiv.org/abs/2609.30591

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