On Quasitoric Orbifolds
On Quasitoric Orbifolds
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关于拟定轨道折叠
DOI：
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发表时间：
2008
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影响因子：
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通讯作者：
Soumen Sarkar
中科院分区：
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作者：
Mainak Poddar;Soumen Sarkar
准空间是由Davis和Januskiewicz在他们1991年的杜克论文中引入的。在那里，他们广泛研究了拓扑不变量的quasitoric流形。
这些流形是非奇异投射环面簇的推广或拓扑对应。本文研究拟定轨道折叠的结构和不变量。特别地，我们讨论了拟轨道的等价定义，确定了拟轨道的轨道基本群、有理同调群和上同调环。我们确定是否任何拟素轨道可以是一个光滑流形的有限群作用的商或没有。证明了几乎复结构的存在性，并刻画了几乎复拟复轨道的Chen-Ruan上同调群。
Quasitoric spaces were introduced by Davis and Januskiewicz in their 1991 Duke paper. There they extensively studied topological invariants of quasitoric manifolds.
These manifolds are generalizations or topological counterparts of nonsingular projective toric varieties. In this article we study structures and invariants of quasitoric orbifolds. In particular, we discuss equivalent definitions and determine the orbifold fundamental group, rational homology groups and cohomology ring of a quasitoric orbifold. We determine whether any quasitoric orbifold can be the quotient of a smooth manifold by a finite group action or not. We prove existence of stable almost complex structure and describe the Chen-Ruan cohomology groups of an almost complex quasitoric orbifold.