Contact open books with flexible pages

Abstract

We give an elementary topological obstruction for a manifold $M$ of dimension $2q+1\ge 7$ to admit a contact open book with flexible Weinstein pages and $c_1({\pi }_2(M))=0$: if the torsion subgroup of the $q$-th integral homology group is non-zero, then no such contact open book exists. We achieve this by proving that a symplectomorphism of a flexible Weinstein manifold acts trivially on cohomology. We also produce examples of non-trivial loops of flexible contact structures using related ideas.

Improved exposition following referee's comments. To appear in the Bulletin of the London Mathematical Society. 10 pages

References in corpus (3)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Symplectic homology and the Eilenberg-Steenrod axioms
• Subflexible symplectic manifolds