Tight Planar Contact Manifolds with Vanishing Heegaard Floer Contact Invariants

TL;DR

This paper constructs infinite families of tight, non-fillable contact manifolds supported by planar open books, with some being hyperbolic, all exhibiting vanishing Heegaard Floer contact invariants, advancing understanding of contact topology.

Contribution

It introduces new infinite families of tight, non-fillable contact manifolds with vanishing invariants, including hyperbolic examples, expanding the landscape of known contact structures.

Findings

Infinite families of tight, non-fillable contact manifolds with vanishing invariants.

Existence of hyperbolic examples among these families.

Support by planar open books with specific properties.

Abstract

In this note, we exhibit infinite families of tight non-fillable contact manifolds supported by planar open books with vanishing Heegaard Floer contact invariants. Moreover, we also exhibit an infinite such family where the supported manifold is hyperbolic.