The topology of toric origami manifolds
| Autor: | Ana Rita Pires, Tara S. Holm |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
General Mathematics
010102 general mathematics Torus Topology Mathematics::Geometric Topology Mathematics::Algebraic Topology 01 natural sciences Cohomology Manifold Computer Science::Emerging Technologies Hypersurface 0103 physical sciences Equivariant cohomology Mathematics::Differential Geometry 010307 mathematical physics 0101 mathematics Degeneracy (mathematics) Mathematics::Symplectic Geometry Topology (chemistry) Mathematics Symplectic geometry |
| Zdroj: | Mathematical Research Letters. 20:885-906 |
| ISSN: | 1945-001X 1073-2780 |
| Popis: | 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 co-orientable folding hypersurface. We prove that the cohomology is concentrated in even degrees, and that the equivariant cohomology satisfies the GKM description. Finally we show that toric origami manifolds with co-orientable folding hypersurface provide a class of examples of Masuda and Panov's torus manifolds. |
| Databáze: | OpenAIRE |
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