Gluing Tight Contact Structures

نویسنده

  • KO HONDA
چکیده

We prove gluing theorems for tight contact structures. As special cases, we rederive gluing theorems due to V. Colin and S. Makar-Limanov and present an algorithm for determining whether a given contact structure on a handlebody is tight. As applications, we construct a tight contact structure on a genus 4 handlebody which becomes overtwisted after Legendrian −1 surgery and study certain Legendrian surgeries on T 3.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Convex Decomposition Theory 3

We use convex decomposition theory to (1) reprove the existence of a universally tight contact structure on every irreducible 3-manifold with nonempty boundary, and (2) prove that every toroidal 3-manifold carries infinitely many nonisotopic, nonisomorphic tight contact structures. It has been known for some time that there are deep connections between the theory of taut foliations and tight co...

متن کامل

Contact Structures on Elliptic

We show that an oriented elliptic 3-manifold admits a universally tight positive contact structure iff the corresponding group of deck transformations on S preserves a standard contact structure pointwise. We also relate universally tight contact structures on 3-manifolds covered by S to the exceptional isomorphism SO(4) = (SU(2) × SU(2))/±1. The main tool used is equivariant framings of 3-mani...

متن کامل

On the Coarse Classification of Tight Contact Structures

We present a sketch of the proof of the following theorems: (1) Every 3-manifold has only finitely many homotopy classes of 2-plane fields which carry tight contact structures. (2) Every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures. In this article we explain how to normalize tight contact structures with respect to a fixed triangulation. Using t...

متن کامل

Tight Contact Structures on Lens Spaces

In this paper we develop a method for studying tight contact structures on lens spaces. We then derive uniqueness and non-existence statements for tight contact structures with certain (half) Euler classes on lens spaces.

متن کامل

O ct 2 00 1 TIGHT CONTACT STRUCTURES ON FIBERED HYPERBOLIC 3 - MANIFOLDS

We take a first step towards understanding the relationship between foliations and universally tight contact structures on hyperbolic 3-manifolds. If a surface bundle over a circle has pseudo-Anosov holonomy, we obtain a classification of “extremal” tight contact structures. Specifically, there is exactly one contact structure whose Euler class, when evaluated on the fiber, equals the Euler num...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2001