The cohomology of real Grassmannians via Schubert stratifications

Eric Berry; Scotty Tilton

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arXiv · 2011.07695

The cohomology of real Grassmannians via Schubert stratifications

Eric Berry·Scotty Tilton

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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.

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Eric Berry, Scotty Tilton. 2020-11-16. The cohomology of real Grassmannians via Schubert stratifications. https://arxiv.org/abs/2011.07695

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