Homotopy types of partial quotients for a certain case

TL;DR

This paper determines the homotopy type of a specific quotient space derived from a moment-angle complex under a diagonal circle action, contributing to the understanding of topological properties of these spaces.

Contribution

It explicitly identifies the homotopy type of the quotient space for a certain class of moment-angle complexes, advancing topological classification methods.

Findings

Homotopy type of the quotient space is explicitly determined.

Provides new insights into the topology of moment-angle complexes.

Enhances understanding of the effects of circle actions on topological spaces.

Abstract

In this paper, we determine the homotopy type of the quotient space $\mathcal{Z}_{\Delta^k_m}/S^1_d$, given by the moment-angle complex $\mathcal{Z}_{\Delta_m^k}$ under the diagonal circle action.