Topological complexity of symplectic manifolds

Mark Grant, Stephan Mescher

Published 2018-02-13Version 1

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. Since symplectically hyperbolic manifolds are symplectically atoroidal, we obtain many new calculations of topological complexity, including iterated surface bundles and symplectically aspherical manifolds with hyperbolic fundamental groups.