Formality in cosymplectic and Sasakian geometries

Marisa Fernandez

In this talk, we give conditions under which a mapping torus, not necessarily symplectic, has a non-zero Massey product. We apply this to prove that there are non-formal compact cosymplectic manifolds of dimension $m$ $(=2n+1)$ and with first Betti number $b$ if and only if $m=3$ and $b \geq 2$, or $m \geq 5$ and $b \geq 1$. On the other hand, we prove that all higher Massey products on any simply connected Sasakian manifold vanish. Nevertheless, for every $n\geq3$, we exhibit the first examples of simply connected compact Sasakian manifolds of dimension $2n+1$ which are non-formal because they have a non-zero triple Massey product. (Joint work with G. Bazzoni, I. Biswas, V. Munoz and A. Tralle)

http://scgp.stonybrook.edu/video_portal/video.php?id=1342

Simons- Workshop: G2 manifolds