Hyperbolic 3-manifolds admitting no fillable contact structures

TL;DR

This paper identifies infinite hyperbolic 3-manifolds that do not support weakly symplectically fillable contact structures, using Heegaard Floer theory, while noting some admit tight contact structures.

Contribution

It demonstrates the existence of hyperbolic 3-manifolds with no fillable contact structures, expanding understanding of contact topology in hyperbolic geometry.

Findings

Infinite hyperbolic 3-manifolds with no fillable contact structures

Some of these manifolds admit tight contact structures

Application of Heegaard Floer theory to contact topology

Abstract

In this paper, we find infinite hyperbolic 3-manifolds that admit no weakly symplectically fillable contact structures, using tools in Heegaard Floer theory. We also remark that part of these manifolds do admit tight contact structures.