Topological complexity of symplectic manifolds
Topological complexity of symplectic manifolds
复制标题
辛流形的拓扑复杂性
DOI：
10.1007/s00209-019-02366-x
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发表时间：
2018
影响因子：
0.8
通讯作者：
Stephan Mescher
中科院分区：
文献类型：
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作者：
Mark Grant;Stephan Mescher
我们证明了每个辛阿托流形的拓扑复杂性等于其维度的两倍。这是Rudyak和Oprea的一个结果的拓扑复杂性的类比，他们证明了辛非球面的Lusternik-Schnirelmann范畴等于它的维度。辛双曲流形是辛阿托型的，其基本群不包含二阶自由阿贝尔子群的辛非球面流形也是辛阿托型的。由此，我们得到了许多新的拓扑复杂性计算方法，包括迭代曲面丛和具有双曲基本群的辛非球面流形。
We prove that the topological complexity of every symplectically atoroidal manifold is equal to twice its dimension. This is the analogue for topological complexity of a result of Rudyak and Oprea, who showed that the Lusternik–Schnirelmann category of a symplectically aspherical manifold equals its dimension. Symplectically hyperbolic manifolds are symplectically atoroidal, as are symplectically aspherical manifolds whose fundamental group does not contain free abelian subgroups of rank two. Thus we obtain many new calculations of topological complexity, including iterated surface bundles and symplectically aspherical manifolds with hyperbolic fundamental groups.
DOI：
10.1090/s0002-9939-08-09529-4
发表时间：
2007-06
期刊：
arXiv: Algebraic Topology
影响因子：
--
作者：
M. Farber;Mark Grant
通讯作者：
M. Farber;Mark Grant