The cohomology of real Grassmannians via Schubert stratifications
arXiv:2011.07695
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.
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