Equivariant $K$-theory of cellular toric bundles and related spaces

TL;DR

This paper computes the equivariant and ordinary topological K-theory rings of toric bundles with cellular toric fibers, extending previous results to more general spaces like toroidal horospherical embeddings.

Contribution

It generalizes the K-theory description of smooth projective toric bundles to cellular toric varieties and applies these results to toroidal horospherical embeddings.

Findings

Explicit description of equivariant K-theory for cellular toric bundles

Extension of K-theory results to toroidal horospherical embeddings

Provides tools for computing K-theory in more complex geometric settings

Abstract

In this article we describe the equivariant and ordinary topological $K$-ring of a toric bundle with fiber a $T$-{\it cellular} toric variety. This generalizes the results in \cite{su} on $K$-theory of smooth projective toric bundles. We apply our results to describe the equivariant topological $K$-ring of a toroidal horospherical embedding.