Topological classification of quasitoric manifolds with the second Betti number 2

TL;DR

This paper classifies quasitoric manifolds with second Betti number 2, showing they are distinguished by their cohomology rings up to homeomorphism, thus advancing topological understanding of these manifolds.

Contribution

It provides a topological classification of quasitoric manifolds with , highlighting the role of cohomology rings in their distinction.

Findings

Quasitoric manifolds with  are classified topologically.

Cohomology rings uniquely distinguish these manifolds up to homeomorphism.

The classification advances understanding of the topology of quasitoric manifolds.

Abstract

A quasitoric manifold is a $2n$-dimensional compact smooth manifold with a locally standard action of an $n$-dimensional torus whose orbit space is a simple polytope. In this article, we classify quasitoric manifolds with the second Betti number $\beta_2=2$ topologically. Interestingly, they are distinguished by their cohomology rings up to homeomorphism.