Topological classification of quasitoric manifolds with second Betti number 2

Suyoung Choi, Seonjeong Park and Dong Youp Suh

Vol. 256 (2012), No. 1, 19–49

DOI: 10.2140/pjm.2012.256.19

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. We classify quasitoric manifolds with second Betti number β₂ = 2 topologically. Interestingly, they are distinguished by their cohomology rings up to homeomorphism.

Keywords

quasitoric manifolds, generalized Bott manifold, cohomological rigidity, moment angle manifold, toric topology

Mathematical Subject Classification 2010

Primary: 57R19, 57R20, 57S25

Secondary: 14M25

Milestones

Received: 14 March 2011

Revised: 2 September 2011

Accepted: 5 September 2011

Published: 6 May 2012