Some Open Book and Contact Structures on Moment-Angle Manifolds

TL;DR

This paper constructs open book decompositions on all moment-angle manifolds, describes their topology, and proves that all odd-dimensional ones admit contact structures, contrasting with the rarity of symplectic structures in even dimensions.

Contribution

It introduces a universal method to build open book structures on moment-angle manifolds and establishes the existence of contact structures on all odd-dimensional cases.

Findings

All odd-dimensional moment-angle manifolds admit contact structures.

Open book structures are constructed on all moment-angle manifolds.

Most even-dimensional moment-angle manifolds do not admit symplectic structures.

Abstract

We construct open book structures on all moment-angle manifolds and describe the topology of their leaves and bindings under certain restrictions. II. We also show, using a recent deep result about contact forms due to Borman, Eliashberg and Murphy [6], that every odd-dimensional moment-angle manifold admits a contact structure. This contrasts with the fact that, except for a few, well-determined cases, even-dimensional ones do not admit symplectic structures. We obtain the same results for large families of more general intersections of quadrics.