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Simplicial volume of open books in dimension 4
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In this short note we adapt a proof by Bucher and Neofytidis to prove that the simplicial volume of 4-manifolds admitting an open book decomposition vanishes. In particular this shows that Quinns signature invariant, which detects the existence of an open book decomposition in dimensions above 4, is insufficient to characterize open books in dimension 4, even if one allows arbitrary stabilizations via connected sums.
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Handle decompositions and stabilizations of open books
A handle-exchange construction produces new open book decompositions in all dimensions n≥3 and shows every trivial-monodromy open book stabilizes to a page made of trivial disk bundles over spheres.
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