Manifolds | 3-manifolds | Differential geometry
In mathematics, a Haken manifold is a compact, P²-irreducible 3-manifold that is sufficiently large, meaning that it contains a properly embedded two-sided incompressible surface. Sometimes one considers only orientable Haken manifolds, in which case a Haken manifold is a compact, orientable, irreducible 3-manifold that contains an orientable, incompressible surface. A 3-manifold finitely covered by a Haken manifold is said to be virtually Haken. The Virtually Haken conjecture asserts that every compact, irreducible 3-manifold with infinite fundamental group is virtually Haken. This conjecture was proven by Ian Agol. Haken manifolds were introduced by Wolfgang Haken. proved that Haken manifolds have a hierarchy, where they can be split up into 3-balls along incompressible surfaces. Haken also showed that there was a finite procedure to find an incompressible surface if the 3-manifold had one. William Jaco and Ulrich Oertel gave an algorithm to determine if a 3-manifold was Haken. Normal surfaces are ubiquitous in the theory of Haken manifolds and their simple and rigid structure leads quite naturally to algorithms. (Wikipedia).
What is a Manifold? Lesson 6: Topological Manifolds
Topological manifolds! Finally! I had two false starts with this lesson, but now it is fine, I think.
From playlist What is a Manifold?
Hausdorff School: Introduction by Karl-Theodor Sturm
Presentation of the Hausdorff School by Karl-Theodor Sturm, coordinator of the Hausdorff Center. The “Hausdorff School for Advanced Studies in Mathematics” is an innovative new program for postdocs by the Hausdorff Center. The official inauguration took place on October 20, 2015.
From playlist Inauguration of Hausdorff School 2015
Hausdorff School: Lecture by Jean-Pierre Bourguignon
Inauguration of the Hausdorff School The “Hausdorff School for Advanced Studies in Mathematics” is an innovative new program for postdocs by the Hausdorff Center. The official inauguration took place on October 20, 2015. Lecture by Jean-Pierre Bourguignon on "Sound, Shape, and Harmony –
From playlist Inauguration of Hausdorff School 2015
An introduction to the Gromov-Hausdorff distance
Title: An introduction to the Gromov-Hausdorff distance Abstract: We give a brief introduction to the Hausdorff and Gromov-Hausdorff distances between metric spaces. The Hausdorff distance is defined on two subsets of a common metric space. The Gromov-Hausdorff distance is defined on any
From playlist Tutorials
Manifolds 1.1 : Basic Definitions
In this video, I give the basic intuition and definitions of manifolds. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Manifolds
Minerva Lectures 2012 - Ian Agol Talk 1: The virtual Haken conjecture: 3-manifold topology
Talk one of the second Minerva lecture series, by Prof. Ian Agol on October 22rd, 2012 at the Mathematics Department, Princeton University. More information available at: http://www.math.princeton.edu/events/seminars/minerva-lectures/minerva-lectures-i-virtual-haken-conjecture-overview-3-
From playlist Minerva Lectures - Ian Agol
Ahlfors-Bers 2014 "Surface Subgroups, Cube Complexes, and the Virtual Haken Theorem"
Jeremy Kahn (CUNY Graduate Center): In a largely expository talk, I will summarize the results leading up to the Virtual Haken and Virtual Fibered Theorem for three manifolds, including 1. The Geometrization Theorem of Thurston and Perelman 2. The Surface Subgroup Theorem of the speaker an
From playlist The Ahlfors-Bers Colloquium 2014 at Yale
Hausdorff Example 1: Cofinite Topology
Point Set Topology: We recall the notion of a Hausdorff space and consider the cofinite topology as a source of non-Hausdorff examples. We also note that this topology is always compact.
From playlist Point Set Topology
Tejas Kalelkar: An Algorithm to Identify Hyperbolic Manifolds from Their Geometric Triangulations
Tejas Kalelkar, Indian Institute of Science Education and Research Pune Title: An Algorithm to Identify Hyperbolic Manifolds from Their Geometric Triangulations Abstract: A geometric triangulation of a Riemannian manifold is a triangulation by totally geodesic simplexes. Any two triangulat
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Joel Hass - Lecture 2 - Algorithms and complexity in the theory of knots and manifolds - 19/06/18
School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Joel Hass (University of California at Davis, USA) Algorithms and complexity in the theory of knots and manifolds Abstract: These lectures will introduce algorithmic pro
From playlist Joel Hass - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects
Minerva Lectures 2012 - Ian Agol Talk 2: The virtual Haken conjecture & geometric group theory
Talk two of the second Minerva lecture series, by Prof. Ian Agol on October 23rd, 2012 at the Mathematics Department, Princeton University. More information available at: http://www.math.princeton.edu/events/seminars/minerva-lectures/minerva-lecture-ii-virtual-haken-conjecture-what-geomet
From playlist Minerva Lectures - Ian Agol
Interview at Cirm: Genevieve WALSH
Genevieve Walsh - Mathematician Department of Mathematics - Tufts University Spring 2018 Chaire Jean-Morlet CIRM Expertise: Hyperbolic manifolds and orbifolds, low-dimensional topology, group actions Research: 'I am a geometric topologist, and I'm interested in problems in both geometr
From playlist Topology
Joel Hass - Lecture 4 - Algorithms and complexity in the theory of knots and manifolds - 21/06/18
School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Joel Hass (University of California at Davis, USA) Algorithms and complexity in the theory of knots and manifolds Abstract: These lectures will introduce algorithmic pro
From playlist Joel Hass - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects
Knots, three-manifolds and instantons – Peter Kronheimer & Tomasz Mrowka – ICM2018
Plenary Lecture 11 Knots, three-manifolds and instantons Peter Kronheimer & Tomasz Mrowka Abstract: Over the past four decades, input from geometry and analysis has been central to progress in the field of low-dimensional topology. This talk will focus on one aspect of these developments
From playlist Plenary Lectures
Manifolds 1.3 : More Examples (Animation Included)
In this video, I introduce the manifolds of product manifolds, tori/the torus, real vectorspaces, matrices, and linear map spaces. This video uses a math animation for visualization. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/5koj5
From playlist Manifolds
The Four-Color Theorem and an Instanton Invariant for Spatial Graphs I - Peter Kronheimer
Peter Kronheimer Harvard University October 13, 2015 http://www.math.ias.edu/seminars/abstract?event=83214 Given a trivalent graph embedded in 3-space, we associate to it an instanton homology group, which is a finite-dimensional Z/2 vector space. The main result about the instanton hom
From playlist Geometric Structures on 3-manifolds
Four Color Theorem via Gauge Theory and Three Manifold Topology - Tom Mrowka [2016]
slides for this talk: https://drive.google.com/file/d/1o-WQOW5Dwec5AmMNelfaJAu4KxOS4vdm/view?usp=sharing Name: Tom Mrowka Event: Workshop: Recent Developments in the Mathematical study of Gauge Theory Event URL: view webpage Title: An approach to the Four Color Theorem via Gauge Theory an
From playlist Mathematics
Manifolds - Part 3 - Hausdorff Spaces
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From playlist Manifolds