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 ${C}^{n}{\left(m\right)}^{\ast }$ 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