Related papers: Contact surgery distance

We calculate the bridge distance for $m$-bridge knots/links in the $3$-sphere with sufficiently complicated $2m$-plat projections. In particular we show that if the underlying braid of the plat has $n - 1$ rows of twists and all its…

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…

We construct a simple topological invariant of certain 3-manifolds, including quotients of the 3-sphere by finite groups, based on the fact that the tangent bundle of an orientable 3-manifold is trivialisable. This invariant is strong…

Let $M$ be a smooth manifold with $\dim M\geq 3$ and a base point $x_{0}$. Surgeries along the oriented circle $S^{1}\times \{x_{0}\}$ on the product $ S^{1}\times M$ yields two manifolds $\Sigma _{0}M$ and $\Sigma _{1}M$, called the…

It is clear that every rational surgery on a Hopf link in $3$-sphere is a lens space surgery. In this note we give an explicit computation which lens space is a resulting manifold. The main tool we use is the calculus of continued…

The inner product provides a conceptually and algorithmically simple method for calculating the comoving distance between two cosmological objects given their redshifts, right ascension and declination, and arbitrary constant curvature. The…

We show that a contact $(+1)$-surgery along a Legendrian sphere in a flexibly fillable contact manifold ($c_1=0$ if not subcritical) yields a contact manifold that is algebraically overtwisted if the Legendrian's homology class is not…

We define a general procedure extending surgery to manifolds with foliation or Haefliger structure. We find a single obstruction to foliation surgery along an attaching sphere. When unobstructed, the surgery can be chosen to preserve…

It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost…

It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a stellar ball a*S. The study of S/~, two dimensional stellar sphere S with 2-simplexes identified in pairs…

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…

We survey the interactions between foliations and contact structures in dimension three, with an emphasis on sutured manifolds and invariants of sutured contact manifolds. This paper contains two original results: the fact that a closed…

We prove some contact analogs of smooth embedding theorems for closed $\pi$-manifolds. We show that a closed, $k$-connected, $\pi$-manifold of dimension (2n + 1) that bounds a $\pi$-manifold, contact embeds in the $(4n-2k+3)$-dimensional…

Cosymplectic and normal almost contact structures are analogues of symplectic and complex structures that can be defined on 3-manifolds. Their existence imposes strong topological constraints. Generalized geometry offers a natural common…

Following an example discovered by John Berge, we show that there is a 4-component link L \subset (S^1 x S^2)#(S^1 x S^2) so that, generically, the result of Dehn surgery on L is a 3-manifold with two inequivalent genus 2 Heegaard…

A kissing sphere is a sphere that is tangent to a fixed reference ball. We develop in this paper a distance geometry for kissing spheres, which turns out to be a generalization of the classical Euclidean distance geometry.

In geometry, understanding the topologies and the differentiable structures of manifolds in constructive ways is fundamental and important. It is in general difficult, especially for higher dimensional manifolds. The author is interested in…

Let $M$ be a $3$-manifold with connected non-vacuos boundary which is not spherical. Assume that $N$ is another $3$-manifold with vacuous boundary and $N^{\ast}$ is the $3$-manifold obtained by removing from $N$ the interior of a $3$-cell.…

This note explains how to relate some contact geometric operations, such as surgery, to operations on an underlying contact open book. In particular, we shall give a simple proof of the fact that stabilizations of contact open books yield…

Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which…