Tight contact structures on hyperbolic three-manifolds

TL;DR

This paper demonstrates that infinitely many hyperbolic three-manifolds, created through Dehn surgeries on hyperbolic surface bundles over a circle, admit tight contact structures, expanding understanding of contact topology in hyperbolic geometry.

Contribution

It establishes the existence of tight contact structures on a broad class of hyperbolic three-manifolds obtained via specific Dehn surgeries, a novel result in contact topology.

Findings

Existence of tight contact structures on infinitely many hyperbolic 3-manifolds.

Construction method via Dehn surgeries on hyperbolic surface bundles.

Extension of contact topology results to hyperbolic geometries.

Abstract

We show the existence of tight contact structures on infinitely many hyperbolic three-manifolds obtained via Dehn surgeries along sections of hyperbolic surface bundles over circle.