Unitary toric manifolds, multi-fans and equivariant index

Masuda, Mikiya

doi:10.2748/tmj/1178224815

Cited by 83 publications

(113 citation statements)

References 13 publications

Supporting

Mentioning

108

Contrasting

Unclassified

Order By: Relevance

“…The symplectic or algebraic structure is dropped, and the focus is the existence of an effective smooth action of a torus half the dimension of the manifold. Examples of such topological analogues, from most restrictive to most general, are toric manifolds [8] (referred to by some authors as quasitoric manifolds), topological toric manifolds [20] and torus manifolds [23]. We now show that acyclic toric origami manifolds fit into the framework of torus manifolds, and that Theorem 3.6 also follows from the work of Masuda and Panov on the cohomology of torus manifolds [24].…”

Section: Toric Origami Manifolds Are Locally Standardmentioning

confidence: 80%

The topology of toric origami manifolds

Holm

Pires

2013

Mathematical Research Letters

View full text Add to dashboard Cite

Abstract. A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami symplectic manifolds, studied by Cannas da Silva, Guillemin and Pires, who classified toric origami manifolds by combinatorial origami templates. In this paper, we examine the topology of toric origami manifolds that have acyclic origami template and coörientable folding hypersurface. We prove that the cohomology is concentrated in even degrees, and that the equivariant cohomology satisfies the Goresky, Kottwitz and MacPherson description. Finally, we show that toric origami manifolds with coörientable folding hypersurface provide a class of examples of Masuda and Panov's torus manifolds.

show abstract

Section: Toric Origami Manifolds Are Locally Standardmentioning

confidence: 80%

The topology of toric origami manifolds

Holm

Pires

2013

Mathematical Research Letters

View full text Add to dashboard Cite

show abstract

“…For instance, CP 2 #CP 2 is a quasitoric manifold with an appropriate action of (S 1 ) 2 but not a toric manifold because it does not allow a complex structure (even an almost complex structure). See [23,Section 5] for examples of quasitoric manifolds which are not toric but allow an almost complex structure invariant under the torus action.…”

Section: Quasitoric Manifoldsmentioning

confidence: 99%

Classification problems of toric manifolds via topology

Masuda¹,

Suh²

2008

Toric Topology

Self Cite

View full text Add to dashboard Cite

show abstract

“…For example, for every two complex toric manifolds of complex dimension 2, their equivariant connected sum along a free orbit supports an invariant almost complex structure, has fixed points, but is not (equivariantly diffeomorphic to) a toric manifold; see [10,Section 11.2]. For higher-dimensional analogues, see [6,Section 13]; for more interesting four-dimensional examples, see [14,Theorem 5.1]. A necessary and sufficient condition for a quasitoric manifold to admit an invariant almost complex structure was given in [13, Theorem 1].…”

Section: Remarkmentioning

confidence: 99%