4-manifolds and non-existence of open book
Geometric Topology
2025-09-19 v1
Abstract
Following a recent work of Kastenholz, we show existence of infinitely many parallelizable closed oriented 4-manifolds, none of which admit an open book decomposition. This implies there is no analogue of the Giroux correspondence for Engel manifolds. In particular, not every Engel manifold has a supporting open book, in the sense of Colin, Presas and Vogel.
Keywords
Cite
@article{arxiv.2509.14299,
title = {4-manifolds and non-existence of open book},
author = {Shital Lawande and Kuldeep Saha},
journal= {arXiv preprint arXiv:2509.14299},
year = {2025}
}