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.
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