Topological toric manifolds
Topological toric manifolds
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DOI：
10.17323/1609-4514-2013-13-1-57-98
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发表时间：
2010-12
期刊：
影响因子：
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通讯作者：
Hiroaki Ishida;Yukiko Fukukawa;M. Masuda
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文献类型：
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作者：
Hiroaki Ishida;Yukiko Fukukawa;M. Masuda
我们引入了拓扑环面流形和拓扑扇的概念，并证明了全向拓扑环面流形和完全非奇异拓扑扇之间存在一个双射。拓扑复曲面流形是复曲面流形的一个拓扑类似物，拓扑复曲面流形的族比复曲面流形的族大得多。拓扑扇是一种组合对象，它推广了复曲面几何中单纯扇的概念。在本文之前，已经引入了环面流形的两个拓扑类似物。一个是拟素流形，另一个是环面流形。之前的概念与拓扑环面流形的一个主要区别是前者支持$S^1$-环面的光滑作用，而后者支持$\C^*$-环面的光滑作用。并详细讨论了它们之间的关系。
We introduce the notion of a topological toric manifold and a topological fan and show that there is a bijection between omnioriented topological toric manifolds and complete non-singular topological fans. A topological toric manifold is a topological analogue of a toric manifold and the family of topological toric manifolds is much larger than that of toric manifolds. A topological fan is a combinatorial object generalizing the notion of a simplicial fan in toric geometry. Prior to this paper, two topological analogues of a toric manifold have been introduced. One is a quasitoric manifold and the other is a torus manifold. One major difference between the previous notions and topological toric manifolds is that the former support a smooth action of an $S^1$-torus while the latter support a smooth action of a $\C^*$-torus. We also discuss their relation in details.