Fibered knots and links | Torus knots and links | Algebraic topology

Torus knot

In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies on the surface of a torus in the same way. Each torus knot is specified by a pair of coprime integers p and q. A torus link arises if p and q are not coprime (in which case the number of components is gcd(p, q)). A torus knot is trivial (equivalent to the unknot) if and only if either p or q is equal to 1 or −1. The simplest nontrivial example is the (2,3)-torus knot, also known as the trefoil knot. (Wikipedia).

Torus knot
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Torus knots

http://shpws.me/vr9k Joint work with Saul Schleimer.

From playlist 3D printing

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Torus Magic

Buy at http://www.shapeways.com/shops/GeometricToy Torus Magic is a transformable torus. This torus object is constructed with many rings,and transforms flat,spherical etc. Also you can turn inside out the torus. Copyright (c) 2014,AkiraNishihara

From playlist 3D printed toys

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Two way necklace.torus toy

necklace,two way,Torus by Villarceau circles,mobius ball

From playlist Handmade geometric toys

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Torus Knots explained!

In this video we'll look at how to construct a torus, or trefoil knot. Torus knots are not too hard to understand and they look very cool and can serve as the basis of many cool effects. Twitter: @The_ArtOfCode Facebook: https://www.facebook.com/groups/theartofcode/ Patreon: https://www.

From playlist ShaderToy Tutorials

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Torus Magic with Ring 1

Buy at http://www.shapeways.com/shops/GeometricToy "Torus Magic" can eat another torus.This torus object is constructed with 30 large rings(70mm diameter) and many small rings. Copyright (c) 2015,AkiraNishihara

From playlist 3D printed toys

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Gluing a Torus

Gluing is a good method to construct new topological spaces from known ones. Here a rectangles is glued along the edges to form a torus. Often the fundamental group of the glued object can be calculated from the pieces (here a rectangles) and the glue (here two intersecting circles). Th

From playlist Algebraic Topology

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Torus Magic 2

The torus magic is constructed with many rings. It transforms flat,spherical,etc. Farther more you can turn it inside out.

From playlist Handmade geometric toys

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Torus Magic with Ring 2

Buy at http://www.shapeways.com/shops/GeometricToy "Torus Magic" can eat another torus.This torus object is constructed with 30 large rings(70mm diameter) and many small rings. Copyright (c) 2015,AkiraNishihara

From playlist 3D printed toys

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Legendrian Torus and Cable Links - Lisa Traynor

Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Legendrian Torus and Cable Links Speaker: Lisa Traynor Affiliation: Bryn Mawr College Date: November 22, 2021 Legendrian torus knots were classified by Etnyre and Honda. I will explain the classification of Legendrian toru

From playlist Mathematics

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Hyperbolic Knot Theory (Lecture - 2) by Abhijit Champanerkar

PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl

From playlist Knots Through Web (Online)

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Toroflux paradox: making things (dis)appear with math

NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Today is all about geometric appearing and vanishing paradoxes and that math that powers them. This vide

From playlist Recent videos

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Satellite operations and Legendrian knot theory - John Etnyre

Satellite operations and Legendrian knot theory Augmentations and Legendrians at the IAS Topic: Satellite operations and Legendrian knot theory Speaker: John Etnyre Date: Thursday, February 11 Satellite operations are a common way to create interesting knot types in the smooth category. I

From playlist Mathematics

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Colin Adams: Hyperbolic Volumes of Virtual Knots and their Compositions

Colin Adams, Williams College Title: Hyperbolic Volumes of Virtual Knots and their Compositions Hyperbolic Volumes of Virtual Knots and their Compositions\\ \noindent\textbf{Abstract:} Many knots are known to be hyperbolic and therefore have a hyperbolic volume. But composite knots are n

From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

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Andrew Lobb: Quantum sln knot cohomology and the slice genus

Abstract: We will give an overview of the information about the smooth slice genus so far yielded by the quantum 𝔰𝔩n knot cohomologies. Recording during the thematic meeting "Knotted Embeddings in Dimensions 3 and 4" the February 15, 2017 at the Centre International de Rencontres Mathémat

From playlist Topology

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András Stipsicz - Upsilon invariants of knots

June 22, 2018 - This talk was part of the 2018 RTG mini-conference Low-dimensional topology and its interactions with symplectic geometry

From playlist 2018 RTG mini-conference on low-dimensional topology and its interactions with symplectic geometry I

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MAE5790-14 Global bifurcations of cycles

Hopf, saddle-node bifurcation of cycles, SNIPER, and homoclinic bifurcation. Coupled oscillators. Knotted cycles. Quasiperiodicity. Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 8.4, 8.6.

From playlist Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University

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Turn a Torus Inside Out

Buy at http://www.shapeways.com/shops/GeometricToy This object consists of two "Torus Magic".These torus objects are constructed with 30 large rings(70mm diameter) and many small rings. Copyright (c) 2015,Akira Nishihara

From playlist 3D printed toys

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Jessica Purcell: Structure of hyperbolic manifolds - Lecture 1

Abstract: In these lectures, we will review what it means for a 3-manifold to have a hyperbolic structure, and give tools to show that a manifold is hyperbolic. We will also discuss how to decompose examples of 3-manifolds, such as knot complements, into simpler pieces. We give conditions

From playlist Topology

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