On the classification of quasitoric manifolds over dual cyclic polytopes

Hasui, Sho

doi:10.2140/agt.2015.15.1387

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On the classification of quasitoric manifolds over dual cyclic polytopes

Sho Hasui

Algebraic & Geometric Topology 15 (2015) 1387–1437

DOI: 10.2140/agt.2015.15.1387

Abstract

For a simple $n$ –polytope $P$ , a quasitoric manifold over $P$ is a $2 n$ –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 $C^{n} {(m)}^{*}$ 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

Volume 15, issue 3 (2015)