The topology of toric origami manifolds
The topology of toric origami manifolds
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环面折纸流形的拓扑
DOI：
10.4310/mrl.2013.v20.n5.a6
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
A. R. Pires
中科院分区：
文献类型：
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作者：
T. Holm;A. R. Pires
流形上的折叠辛形式是一种封闭的 2 形式，沿着超曲面具有尽可能温和的简并性。一类特殊的折叠辛流形是折纸辛流形，由 Cannas da Silva、Guillemin 和 Pires 研究，他们通过组合折纸模板对环面折纸流形进行分类。在本文中，我们研究了具有非循环折纸模板和可共向折叠超曲面的环面折纸流形的拓扑。我们证明了上同调集中在偶次，并且等变上同调满足 GKM 描述。最后，我们证明具有可共向折叠超曲面的环面折纸流形提供了一类 Masuda 和 Panov 环面流形的示例。
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.