4-manifolds and non-existence of open book
Shital Lawande, Kuldeep Saha
Published: 2025/9/17
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.