Volume 15, issue 3 (2015)

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On the classification of quasitoric manifolds over dual cyclic polytopes

Sho Hasui

Algebraic & Geometric Topology 15 (2015) 1387–1437
Abstract

For a simple n–polytope P, a quasitoric manifold over P is a 2n–dimensional smooth manifold with a locally standard action of an n–dimensional torus for which the orbit space is identified with P. This paper acheives the topological classification of quasitoric manifolds over the dual cyclic polytope Cn(m) when n > 3 or m n = 3. Additionally, we classify small covers, the “real version” of quasitoric manifolds, over all dual cyclic polytopes.

Keywords
toric topology, quasitoric manifolds, cohomological rigidity
Mathematical Subject Classification 2010
Primary: 57R19, 57S25
References
Publication
Received: 24 November 2013
Revised: 27 April 2014
Accepted: 6 June 2014
Published: 19 June 2015
Authors
Sho Hasui
Department of Mathematics, Faculty of Science
Kyoto University
Sakyo-ku
Kyoto 606-8502
Japan