Nested fibre bundles in Bott-Samelson varieties

TL;DR

This paper provides a topological perspective on Bott-Samelson varieties, analyzing invariant subspaces under torus action and describing their equivariant cohomology generators, building on prior algebraic results.

Contribution

It offers a topological explanation for key algebraic results on Bott-Samelson varieties and identifies generators of their equivariant cohomology.

Findings

Identification of invariant subspaces under torus action

Topological and homological properties of these subspaces

Explicit description of equivariant cohomology generators

Abstract

We give a topological explanation of the main results of V.Shchigolev, Categories of Bott-Samelson Varieties, Algebras and Representation Theory, 23 (2), 349-391, 2020. To this end, we consider some subspaces of Bott-Samelson varieties invariant under the action of the maximal compact torus $K$ and study their topological and homological properties. Moreover, we describe multiplicative generators of the equivariant cohomologies of Bott-Samelson varieties.