Simplicial volume of open books in dimension 4
Geometric Topology
2025-04-16 v1 Algebraic Topology
Abstract
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.
Keywords
Cite
@article{arxiv.2504.10975,
title = {Simplicial volume of open books in dimension 4},
author = {Thorben Kastenholz},
journal= {arXiv preprint arXiv:2504.10975},
year = {2025}
}