English

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