Topological complexity of symplectic manifolds

Mark Grant (Corresponding Author), Stephan Mescher

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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.
Original languageEnglish
Number of pages13
JournalMathematische Zeitschrift
Early online date3 Aug 2019
Publication statusE-pub ahead of print - 3 Aug 2019


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