arXiv 1802.047462018-02math.ATmath.SG

Topological complexity of symplectic manifolds

Mark Grant, Stephan Mescher

备注：: 12 pages, final version, to appear in Math. Z
发表信息：: Math. Z. 295 (2020), no. 1-2, 667-679
DOI：: 10.1007/s00209-019-02366-x

英文摘要：

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. Our result also applies in the greater generality of cohomologically symplectic manifolds.

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