Additivity of factorization algebras & the cohomology of real Grassmannians
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Date
2021
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Montana State University - Bozeman, College of Letters & Science
Abstract
This dissertation is composed of two separate projects. The first chapter proves two additivity results for factorization algebras. These provide a way to understand factorization algebras on the product of two spaces. Our results can be thought of as a generalization of Dunn's additivity for En-algebras. In particular, our methods provide a new proof of Dunn's additivity. The second chapter is an examination of the Schubert stratification of real Grassmann manifolds. We use this extra structure to identify the quasi-isomorphism type of the Schubert CW chain complex for real Grassmannians. We provide explicit computations using our methods.