Examples of toric manifolds which are not quasitoric manifolds

Abstract

We construct toric manifolds of complex dimension $\ge 4$, whose orbit spaces by the action of the compact torus are not homeomorphic to simple polytopes (as manifolds with corners). These provide the first known examples of toric manifolds which are not quasitoric manifolds.

9 pages, 12 figures

Cited by in corpus (4)

• Cohomological rigidity of manifolds defined by right-angled 3-dimensional polytopes
• Classification of toric manifolds over an $n$-cube with one vertex cut
• The characterization of $(n-1)$-spheres with $n+4$ vertices having maximal Buchstaber number
• Root systems and symmetries of torus manifolds