Lemmas | 3-manifolds

Dehn's lemma

In mathematics, Dehn's lemma asserts that a piecewise-linear map of a disk into a 3-manifold, with the map's singularity set in the disk's interior, implies the existence of another piecewise-linear map of the disk which is an embedding and is identical to the original on the boundary of the disk. This theorem was thought to be proven by Max Dehn, but Hellmuth Kneser found a gap in the proof. The status of Dehn's lemma remained in doubt until Christos Papakyriakopoulos using work by Johansson (1938) proved it using his "tower construction". He also generalized the theorem to the loop theorem and sphere theorem. (Wikipedia).

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Allison Moore - Essential Conway spheres and Floer homology via immersed curves

38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Allison Moore, Virginia Commonwealth University Title: Essential Conway spheres and Floer homology via immersed curves Abstract: We consider the problem of whether Dehn surgery along a knot in the three-sphere produces an

From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021

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Water and Wine

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt

From playlist Problems, Paradoxes, and Sophisms

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The pi/4 polyhedron

Matthias Goerner's 3D print: http://shpws.me/SZbN Countdown d24: https://youtu.be/U0soSn7BojQ Matthias' version of the construction of the polyhedron: http://www.unhyperbolic.org/sydler.html Demonstration of the Wallace–Bolyai–Gerwien theorem by Dima Smirnov and Zivvy Epstein: https://dmsm

From playlist 3D printing

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The Straw Trick

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt

From playlist Problems, Paradoxes, and Sophisms

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Ignat Soroko - Groups of type FP: their quasi-isometry classes and homological Dehn functions

38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Ignat Soroko, Louisiana State University Title: Groups of type FP: their quasi-isometry classes and homological Dehn functions Abstract: There are only countably many isomorphism classes of finitely presented groups, i.e.

From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021

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Linear Algebra Vignette 4a: Fibonacci Numbers - Review Of The Eigenvalue Decomposition

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt

From playlist Linear Algebra Vignettes

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Class 14: Hinged Dissections

MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This class focuses on hinged dissections. Examples of hinged dissections and several built, reconfigurable applications are offere

From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012

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Linear Algebra Vignette 1a: Matrix Representation of a Linear Transformation

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt

From playlist Linear Algebra Vignettes

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Linear Algebra Vignette 3g: Easy Eigenvalues - The Determinant

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt

From playlist Linear Algebra Vignettes

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Linear Algebra Vignette 3h: Easy Eigenvalues - The Grand Finale

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt

From playlist Linear Algebra Vignettes

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Linear Algebra Vignette 4c: Fibonacci Numbers - The Derivation Of The Formula

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt

From playlist Linear Algebra Vignettes

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Hyperbolic surfaces and their Teichmüller spaces (Lecture – 03) by Subhojoy Gupta

Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b

From playlist Geometry, Groups and Dynamics (GGD) - 2017

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Linear Algebra Vignette 3a: Easy Eigenvalues - Introduction

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt

From playlist Linear Algebra Vignettes

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Taming the hydra: the Word Problem, Dehn functions, and extreme integer compression - Timothy Riley

Taming the hydra: the Word Problem, Dehn functions, and extreme integer compression Timothy Riley Cornell University; Member, School of Mathematics December 2, 2014 For a finitely presented group, the Word Problem asks for an algorithm which declares whether or not words on the generators

From playlist Mathematics

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Piotr Przytycki: Torsion groups do not act on 2-dimensional CAT(0) complexes

We show, under mild hypotheses, that if each element of a finitely generated group acting on a 2-dimensional CAT(0) complex has a fixed point, then the action is trivial. In particular, all actions of finitely generated torsion groups on such complexes are trivial. As an ingredient, we pro

From playlist Geometry

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Cheuk Yu Mak: Spherical Lagrangian submanifolds and spherical functors

The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: Spherical twist is an auto equivalence of a category whose definition is motivated from the Dehn twist along a Lagrangian submanifold inside a symplectic

From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"

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How a Microwave Oven Works

Engineer Rudy Dehn tells us how a magnetron works and how it cooks food in a microwave. Mr. Dehn helped develop both the 915 Mhz and 2.45 Ghz microwave oven at General Electric in the 1960s-80s. He shows us the cathode and anode and describes how microwave energy is created using a filame

From playlist How Things Work

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Linear Algebra Vignette 2a: RREF - What It's For

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt

From playlist Linear Algebra Vignettes

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Dehn Twists Exact Sequences Through Lagrangian Cobordism - Weiwei Wu

Weiwei Wu University of Montreal October 23, 2015 https://www.math.ias.edu/seminars/abstract?event=85044 In this talk we first introduce a new "singularity-free" approach to the proof of Seidel's long exact sequence, including the fixed-point version. This conveniently generalizes to Deh

From playlist PU/IAS Symplectic Geometry Seminar

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Linear Algebra Vignette 3d: Easy Eigenvalues - Linearly Dependent Columns

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt

From playlist Linear Algebra Vignettes

Related pages

Interior (topology) | Tower of objects | Covering space | Mathematics | Loop theorem | 3-manifold | Sphere theorem (3-manifolds) | Embedding | Singularity (mathematics) | Boundary (topology) | Disk (mathematics)