Contact open books with flexible pages

We give an elementary topological obstruction for a manifold M$M$ of dimension 2q+1⩾7$2q+1\geqslant 7$ to admit a contact open book with flexible Weinstein pages and c1(π2(M))=0$c_1(\pi_2(M)) = 0$: if the torsion subgroup of the q$q$‐th integral homology group is non‐zero, then no such contact open...

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Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2023-06, Vol.55 (3), p.1302-1313
Main Authors: Bowden, Jonathan, Crowley, Diarmuid
Format: Article
Language:English
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Summary:We give an elementary topological obstruction for a manifold M$M$ of dimension 2q+1⩾7$2q+1\geqslant 7$ to admit a contact open book with flexible Weinstein pages and c1(π2(M))=0$c_1(\pi_2(M)) = 0$: if the torsion subgroup of the q$q$‐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 integral cohomology. We also produce examples of non‐trivial loops of flexible contact structures using related ideas.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms.12791