$K$-theory of Flag Bott manifolds

TL;DR

This paper provides a detailed description of the topological K-ring of flag Bott manifolds, including generators and relations, and applies these results to flag Bott and Samelson varieties.

Contribution

It offers a new presentation of the topological K-ring and Grothendieck ring for flag Bott and related varieties, advancing understanding of their algebraic topology.

Findings

Explicit generators and relations for the K-ring of flag Bott manifolds

Presentation of the Grothendieck ring of algebraic vector bundles over flag Bott and Samelson varieties

Enhanced understanding of the topological K-theory of these complex manifolds

Abstract

The aim of this paper is to describe the topological $K$-ring, in terms of generators and relations of a flag Bott manifold. We apply our results to give a presentation for the topological K-ring and hence the Grothendieck ring of algebraic vector bundles over flag Bott Samelson varieties.