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arXiv · 2309.00429

Cohomology of complete unordered flag manifolds

Lorenzo Guerra·Santanil Jana
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Abstract

We consider quotients of complete flag manifolds in Cn and Rn by an action of the symmetric group on n objects. We compute their cohomology with field coefficients of any characteristic. Specifically, we show that these topological spaces exhibit homological stability and we provide a closed-form description of their stable cohomology rings. We also describe a simple algorithmic procedure to determine their unstable cohomology additively.

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Lorenzo Guerra, Santanil Jana. 2023-09-01. Cohomology of complete unordered flag manifolds. https://arxiv.org/abs/2309.00429

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