Classification of tight contact structures on surgeries on the figure-eight knot

Abstract

Two of the basic questions in contact topology are which manifolds admit tight contact structures, and on those that do, can we classify such structures. We present the first such classification on an infinite family of (mostly) hyperbolic 3-manifolds: surgeries on the figure-eight knot. We also determine which of the tight contact structures are symplectically fillable and which are universally tight.

arXiv comment47 pages, many color figures; v2: minor corrections, updated title

References in corpus (15)

• On the classification of tight contact structures I
• Right-veering diffeomorphisms of compact surfaces with boundary II
• Lectures on open book decompositions and contact structures
• Structures de contact en dimension trois et bifurcations des feuilletages de surfaces
• A Legendrian surgery presentation of contact 3-manifolds
• On the existence of tight contact structures on Seifert fibered 3-manifolds
• Tight contact structures on fibered hyperbolic 3-manifolds
• Strongly fillable contact 3-manifolds without Stein fillings
• Seifert fibered contact three-manifolds via surgery
• Tight small Seifert fibered manifolds with $e_0=-2$
• Classification of tight contact structures on small Seifert fibered L-spaces
• Pinwheels and bypasses
• A class of tight contact structures on Sigma_2 x I
• Contact Surgeries on the Legendrian Figure-Eight Knot
• Tight contact structures on some plumbed 3-manifolds

Cited by in corpus (3)

• Indefinite Stein fillings and Pin(2)-monopole Floer homology
• Exotic Dehn twists on sums of two contact 3-manifolds
• A monopole invariant for families of contact structures