The topology of Birkhoff varieties
Luke Gutzwiller, Stephen A. Mitchell

TL;DR
This paper proves that Birkhoff varieties are homotopy equivalent to their inclusion in the affine Grassmannian and constructs tubular neighborhoods, providing new insights into their topological structure and equivariant cohomology.
Contribution
It establishes the homotopy equivalence of Birkhoff varieties with their ambient affine Grassmannian and introduces tubular neighborhood constructions for these varieties.
Findings
Birkhoff varieties are homotopy equivalent to their inclusion in the affine Grassmannian
Constructed tubular neighborhoods for Birkhoff and Schubert varieties
Provided observations on torus-equivariant cohomology
Abstract
Our main theorem is that the inclusion of a Birkhoff variety in the affine Grassmannian is a homotopy equivalence. We also construct analogues of tubular neighborhoods for Birkhoff and Schubert varieties. We include some observations on torus-equivariant cohomology.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology
