PreprintCC BY 4.0arXiv
Rational homotopy theory of flag manifolds
Abstract
Let G/P be a flag manifold with G simple. We determine the rational homotopy groups π∗ (G/P)⊗ ℚ and describe the rational cohomology ring H∗ (G/P;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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BibTeX
@misc{duan2026rational,
title = {{Rational homotopy theory of flag manifolds}},
author = {Haibao Duan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.30591},
eprint = {2609.30591},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30591},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Rational homotopy theory of flag manifolds
AU - Haibao Duan
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.30591
UR - https://arxiv.org/abs/2609.30591
AB - Let G/P be a flag manifold with G simple. We determine the rational homotopy groups π_∗ (G/P)⊗ ℚ and describe the rational cohomology ring H^∗ (G/P;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.
ER -