Related papers: Contact surgery numbers
We use the Ozsv\'ath-Szab\'o contact invariants to distinguish between tight contact structures obtained by Legendrian surgeries on stabilized Legendrian links in tight contact 3-manifolds. We also discuss the implication of our result on…
When can one 3-manifold be transformed to another by a finite sequence of Dehn surgeries which are restricted to preserve the first homology of the manifolds ? What is the resulting equivalence relation on 3-manifolds ? What if the surgery…
We first present three graphic surgery formulae for the degree $n$ part $Z_n$ of the Kontsevich-Kuperberg-Thurston universal finite type invariant of rational homology spheres. Each of these three formulae determines an alternate sum of the…
Let $(M,\xi)$ be a contact 3-manifold. We present two new algorithms, the first of which converts an open book $(\Sigma,\Phi)$ supporting $(M,\xi)$ with connected binding into a contact surgery diagram. The second turns a contact surgery…
In this note we show that a closed oriented contact manifold is obtained from the standard contact sphere of the same dimension by contact surgeries on isotropic and coisotropic spheres. In addition, we observe that all closed oriented…
By a result of Eliashberg, every symplectic filling of a three-dimensional contact connected sum is obtained by performing a boundary connected sum on another symplectic filling. We prove a partial generalization of this result for…
It is shown that any closed three-manifold M obtained by integral surgery on a knot in the three-sphere can always be constructed from integral surgeries on a 3-component link L with each component being an unknot in the three-sphere. It is…
We produce a large class of hyperbolic homology 3-spheres admitting arbitrarily many distinct tight contact structures. We also produce a sub-class admitting arbitrarily many distinct tight contact structures within the same homotopy class…
In this paper, we study contact surgeries along Legendrian links in the standard contact 3-sphere. On one hand, we use algebraic methods to prove the vanishing of the contact Ozsv\'{a}th-Szab\'{o} invariant for contact $(+1)$-surgery along…
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…
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.
It is known that every oriented integral homology 3-sphere can be obtained from S^3 by a finite sequence of Borromean surgeries. We give an explicit formula for the variation of the Casson invariant under such a surgery move. The formula…
We show that every tight contact structure on any of the lens spaces $L(ns^2-s+1,s^2)$ with $n\geq 2$, $s\geq 1$, can be obtained by a single Legendrian surgery along a suitable Legendrian realisation of the negative torus knot…
Twists of contact structures in dimension 3 and higher are studied in this paper from a viewpoint of contact round surgery. Three kinds of new modifications of contact structures which are higher-dimensional generalizations of the…
In this paper, we explore minimal contact triangulations on contact 3-manifolds. We give many explicit examples of contact triangulations that are close to minimal ones. The main results of this article say that on any closed oriented…
We study low-dimensional problems in topology and geometry via a study of contact and Cauchy-Riemann ($CR$) structures. A contact structure is called spherical if it admits a compatible spherical $CR$ structure. We will talk about spherical…
We execute Avdek's algorithm to find many algebraically overtwisted and tight $3$-manifolds by contact $+1$ surgeries. In particular, we show that a contact $1/k$ surgery on the standard contact $3$-sphere along any positive torus knot with…
Using the rational surgery formula for the Casson--Walker--Lescop invariant of links in the $3$-sphere, we show that any null-homologous knot in a rational homology sphere admits at most two pairs of integral purely cosmetic surgeries. We…
Let Y(r) be the closed, oriented three-manifold obtained by performing rational r-surgery on the right-handed trefoil knot in the three-sphere. Using contact surgery and the Heegaard Floer contact invariants we construct positive, tight…
In this work, we prove that every complex contact structure gives rise to a distinguished type of almost contact metric 3-structure. As an application of our main result, we provide several new examples of manifolds which admit taut contact…