On the structure of co-K\"ahler manifolds

By the work of Li, a compact co-K\"ahler manifold $M$ is a mapping torus $K_\varphi$, where $K$ is a K\"ahler manifold and $\varphi$ is a Hermitian isometry. We show here that there is always a finite cyclic cover $\bar M$ of the form $\bar M \cong K \times S^1$, where $\cong$ is equivariant diffeomorphism with respect to an action of $S^1$ on $M$ and the action of $S^1$ on $K \times S^1$ by translation on the second factor. Furthermore, the covering transformations act diagonally on $S^1$, $K$ and are translations on the $S^1$ factor. In this way, we see that, up to a finite cover, all compact co-K\"ahler manifolds arise as the product of a K\"ahler manifold and a circle.Comment: 20 pages; revised version: new results on fundamental group of co-K\"ahler manifolds and on compact co-K\"ahler manifolds which are not products. To appear in Geom. Dedicat

A mapping theorem for topological complexity

Peer reviewedPublisher PD

New lower bounds for the topological complexity of aspherical spaces

Date of Acceptance: 5/04/2015 15 pages, 4 figuresPeer reviewedPostprin

The Propagation of Non-Lefschetz Type, The Gottlieb Group and Related Questions

This is a brief note which indicates how the property of being non-Lefschetz may be propagated by equivariant symplectic maps. We also discuss some questions related to the Gottlieb group and nilpotency of symplectic manifolds