The cohomology of real Grassmannians via Schubert stratifications
Abstract
In this paper, we present a closed formula for the cohomology of real Grassmannians. To achieve this, we use a theory of stratified spaces to compute the differentials in a chain complex that computes the cohomology. Specifically, we organize Schubert cells as a conically smooth stratified space in the sense of Ayala, Francis, Tanaka; the links therein yield the sought differentials, using methods in differential topology. Further, we identify the isomorphism type of this chain complex and we use this result to provide a closed formula for the additive structure of the cohomology of real Grassmannians with arbitrary coefficients.
Keywords
Cite
@article{arxiv.2011.07695,
title = {The cohomology of real Grassmannians via Schubert stratifications},
author = {Eric Berry and Scotty Tilton},
journal= {arXiv preprint arXiv:2011.07695},
year = {2020}
}
Comments
Significantly updated version. We proved many of the conjectures from the previous version. In particular, we identity the isomorphism type of the chain complex of real Grassmannians, and provide a closed formula for their cohomology