Tali Pinsky
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View article: Tunnel number one knots satisfy the Berge conjecture
Tunnel number one knots satisfy the Berge conjecture Open
Let $K$ be a tunnel number one knot in $M$ with irreducible knot exterior, where $M$ is either $S^3$, or a connected sum of $S^2\times S^1$ with any lens space. (In particular, this includes $M = S^2\times S^1$.) We prove that if a non-tri…
View article: Rigidity of highly twisted plat diagrams
Rigidity of highly twisted plat diagrams Open
In this paper we prove that if a knot or link has a sufficiently complicated plat projection, then that plat projection is unique. More precisely, if a knot or link has a $2m$-plat projection, where $m$ is at least four, and height at leas…
View article: Graph manifolds that admit arbitrarily many Anosov flows
Graph manifolds that admit arbitrarily many Anosov flows Open
For each natural number n , we construct an example of a graph manifold supporting at least n different Anosov flows that are not orbit equivalent. Our construction is reminiscent of the Thurston-Handel construction [11]: we cut a geodesic…
View article: Arithmetic modular links
Arithmetic modular links Open
We construct a sequence of geodesics on the modular surface such that the complements of the canonical lifts to the unit tangent bundle are arithmetic 3-manifolds.
View article: Analytical study of the Lorenz system: Existence of infinitely many periodic orbits and their topological characterization
Analytical study of the Lorenz system: Existence of infinitely many periodic orbits and their topological characterization Open
We consider the Lorenz equations, a system of three-dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler “geometric model” has been in…
View article: Arithmetic modular links
Arithmetic modular links Open
We construct a sequence of geodesics on the modular surface such that the complement of the canonical lifts to the unit tangent bundle are arithmetic 3-manifolds.
View article: Highly twisted diagrams
Highly twisted diagrams Open
We prove that the knots and links that admit a 3-highly twisted irreducible diagram with more than two twist regions are hyperbolic. This should be compared with a result of Futer-Purcell for 6-highly twisted diagrams. While their proof us…
View article: Analytical study of The Lorenz system: existence of infinitely many periodic orbits and their topological characterization
Analytical study of The Lorenz system: existence of infinitely many periodic orbits and their topological characterization Open
We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been in…
View article: Highly twisted plat diagrams
Highly twisted plat diagrams Open
We prove that the knots and links in the infinite set of $3$-highly twisted $2m$-plats, with $m \geq 2$, are all hyperbolic. This should be compared with a result of Futer-Purcell for $6$-highly twisted diagrams. While their proof uses geo…
View article: Three manifolds that admit infinitely many Anosov flows
Three manifolds that admit infinitely many Anosov flows Open
We construct an example of a graph manifold that supports infinitely many Anosov flows that are not orbit equivalent. Our construction is reminiscent of the Thurston-Handel construction, consisting of cutting open a geodesic flow on a surf…
View article: Graph manifolds that admit arbitrarily many Anosov flows
Graph manifolds that admit arbitrarily many Anosov flows Open
For each natural number n, we construct an example of a graph manifold supporting at least n different Anosov flows that are not orbit equivalent. Our construction is reminiscent of the Thurston-Handel construction: we cut a geodesic flow …
View article: Volumes of Hyperbolic Three-Manifolds Associated with Modular Links
Volumes of Hyperbolic Three-Manifolds Associated with Modular Links Open
Periodic geodesics on the modular surface correspond to periodic orbits of the geodesic flow in its unit tangent bundle PSL 2 ( Z ) ∖ PSL 2 ( R ) . A finite collection of such orbits is a collection of disjoint closed curves in a 3-manifol…
View article: An Upper Bound for the Volumes of Complements of Periodic Geodesics
An Upper Bound for the Volumes of Complements of Periodic Geodesics Open
A periodic geodesic on a surface has a natural lift to the unit tangent bundle; when the complement of this lift is hyperbolic, its volume typically grows as the geodesic gets longer. We give an upper bound for this volume which is linear …
View article: On the topology of the Lorenz system
On the topology of the Lorenz system Open
We present a new paradigm for three-dimensional chaos, and specifically for the Lorenz equations. The main difficulty in these equations and for a generic flow in dimension 3 is the existence of singularities. We show how to use knot theor…
View article: Tunnel number one knots satisfy the Berge Conjecture
Tunnel number one knots satisfy the Berge Conjecture Open
Let $K$ be a tunnel number one knot in $M$ with irreducible knot exterior, where $M$ is either $S^3$, or a connected sum of $S^2\times S^1$ with any lens space. (In particular, this includes $M = S^2\times S^1$.) We prove that if a non-tri…
View article: On the the Berge Conjecture for tunnel number one knots
On the the Berge Conjecture for tunnel number one knots Open
Let $K$ be a tunnel number one knot in $M$, where $M$ is either $S^3$, $S^2\times S^1$, or a connected sum of $S^2\times S^1$ with a lens space. We prove that if a Dehn surgery on $K$ yields a lens space, then $K$ is a doubly primitive kno…
View article: Coding of geodesics and Lorenz-like templates for some geodesic flows
Coding of geodesics and Lorenz-like templates for some geodesic flows Open
We construct a template with two ribbons that describes the topology of all periodic orbits of the geodesic flow on the unit tangent bundle to any sphere with three cone points with hyperbolic metric. The construction relies on the existen…