Cohomology of complete unordered flag manifolds
Algebraic Topology
2023-12-20 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.2309.00429,
title = {Cohomology of complete unordered flag manifolds},
author = {Lorenzo Guerra and Santanil Jana},
journal= {arXiv preprint arXiv:2309.00429},
year = {2023}
}
Comments
37 pages, 2 figures In version 2 the link with representation stability was added and minimal rephrasing and typos correction are performed