English

The topology of Birkhoff varieties

Algebraic Topology 2009-03-30 v3 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.0809.1091,
  title  = {The topology of Birkhoff varieties},
  author = {Luke Gutzwiller and Stephen A. Mitchell},
  journal= {arXiv preprint arXiv:0809.1091},
  year   = {2009}
}

Comments

This is a substantially revised version of an earlier submission. The main results are unchanged, but the proofs have been improved and simplified. We have also corrected an error regarding CW-structures on ind-varieties

R2 v1 2026-06-21T11:17:26.583Z