We give an elementary topological obstruction for a $(2q{+}1)$-manifold $M$ to admit a contact open book with flexible Weinstein pages: 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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