Topological complexity of symplectic manifolds

Mark Grant* (Corresponding Author), Stephan Mescher

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
8 Downloads (Pure)


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
Pages (from-to)667–679
Number of pages13
JournalMathematische Zeitschrift
Early online date3 Aug 2019
Publication statusPublished - Jun 2020

Bibliographical note

Open Access via Springer Compact Agreement.

The authors wish to thank Ay¸se Borat, Michael Farber, Jarek Kedra, and John Oprea for helpful comments regarding an earlier draft of this paper.




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