On cohomology of quasitoric manifolds over a vertex cut of a finite product of simplices

TL;DR

This paper classifies the cohomology rings of quasitoric manifolds over a vertex cut of a product of simplices, providing a detailed algebraic understanding of their topological structure.

Contribution

It introduces a classification of characteristic matrices and cohomology rings for these quasitoric manifolds, expanding the understanding of their algebraic topology.

Findings

Classification of characteristic matrices for these manifolds

Description of their integral cohomology rings

Relations among generators of the cohomology rings

Abstract

In this paper, we classify the characteristic matrices associated to quasitoric manifolds over a vertex cut of a finite product of simplices. We discuss the integral cohomology rings of these quasitoric manifolds with possibly minimal generators and show several relations among the product of these generators. We classify integral cohomology rings (up to isomorphism as graded rings) of the quasitoric manifolds over the vertex cut of a finite product of simplices.