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arXiv · 2106.06253

Contact open books with flexible pages

Jonathan Bowden·Diarmuid Crowley
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Abstract

We give an elementary topological obstruction for a manifold $M$ of dimension $2q{+}1 \geq 7$ 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.

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Jonathan Bowden, Diarmuid Crowley. 2021-06-11. Contact open books with flexible pages. https://doi.org/10.1112/blms.12791

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