Manifolds | Hyperbolic geometry | 3-manifolds | Riemannian manifolds | Kleinian groups
In mathematics, more precisely in topology and differential geometry, a hyperbolic 3–manifold is a manifold of dimension 3 equipped with a hyperbolic metric, that is a Riemannian metric which has all its sectional curvatures equal to -1. It is generally required that this metric be also complete: in this case the manifold can be realised as a quotient of the 3-dimensional hyperbolic space by a discrete group of isometries (a Kleinian group). Hyperbolic 3–manifolds of finite volume have a particular importance in 3–dimensional topology as follows from Thurston's geometrisation conjecture proved by Perelman. The study of Kleinian groups is also an important topic in geometric group theory. (Wikipedia).
Jessica Purcell: Structure of hyperbolic manifolds - Lecture 3
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
Jessica Purcell: Structure of hyperbolic manifolds - Lecture 2
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
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
Julien Duval - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties 2/2
An almost complex manifold is hyperbolic if it does not contain any entire curve. We start characterizing hyperbolic compact almost complex manifolds. These are the ones whose holomorphic discs satisfy a linear isoperimetric inequality. Then we prove the almost complex version of the Greee
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
Julien Duval - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties 1/2
An almost complex manifold is hyperbolic if it does not contain any entire curve. We start characterizing hyperbolic compact almost complex manifolds. These are the ones whose holomorphic discs satisfy a linear isoperimetric inequality. Then we prove the almost complex version of the Greee
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
Low-dimensional dynamics and hyperbolic 3-manifolds - Carvalho
Geometric Structures on 3-manifolds Topic: Low-dimensional dynamics and hyperbolic 3-manifolds Speaker: André de Carvalho Date: Tuesday, January 19 Thurston's hyperbolization of fibered 3-manifolds is based on his classification theorem for isotopy classes of surface homeomorphisms. This
From playlist Mathematics
The circle and projective homogeneous coordinates (cont.) | Universal Hyperbolic Geometry 7b
Universal hyperbolic geometry is based on projective geometry. This video introduces this important subject, which these days is sadly absent from most undergrad/college curriculums. We adopt the 19th century view of a projective space as the space of one-dimensional subspaces of an affine
From playlist Universal Hyperbolic Geometry
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
Hyperbolic Geometry is Projective Relativistic Geometry (full lecture)
This is the full lecture of a seminar on a new way of thinking about Hyperbolic Geometry, basically viewing it as relativistic geometry projectivized, that I gave a few years ago at UNSW. We discuss three dimensional relativistic space and its quadratic/bilinear form, particularly the uppe
From playlist MathSeminars
Robust dynamics, invariant structures and topological classification – Rafael Potrie – ICM2018
Dynamical Systems and Ordinary Differential Equations Invited Lecture 9.11 Robust dynamics, invariant structures and topological classification Rafael Potrie Abstract: Robust dynamical properties imply invariant geometric structures. We will survey the recent advances on topological clas
From playlist Dynamical Systems and ODE
Ian Agol, Lecture 3: Applications of Kleinian Groups to 3-Manifold Topology
24th Workshop in Geometric Topology, Calvin College, June 30, 2007
From playlist Ian Agol: 24th Workshop in Geometric Topology
Fun with finite covers of 3-manifolds - Nathan Dunfield
https://www.math.ias.edu/seminars/abstract?event=47565
From playlist Members Seminar
Nathan Dunfield, Lecture 1: Fun with Finite Covers of 3-Manifolds
33rd Workshop in Geometric Topology, Colorado College, June 9, 2016
From playlist Nathan Dunfield: 33rd Workshop in Geometric Topology
Coarse dynamics and partially hyperbolic diffeomorphisms in 3-manifolds - Rafael Potrie
Members' Seminar Topic: Coarse dynamics and partially hyperbolic diffeomorphisms in 3-manifolds Speaker: Rafael Potrie Affiliation: Universidad de la República, Uruguay; von Neumann Fellow, School of Mathematics Date: February 03, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Jessica Purcell - Lecture 3 - Knots in infinite volume 3-manifolds
Jessica Purcell, Monash University Title: Knots in infinite volume 3-manifolds Classically, knots have been studied in the 3-sphere. However, many examples of knots arising in applications lie in broader classes of 3-manifolds. These include virtual knots, which lie within thickened surfa
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Ian Agol, Lecture 1: Volumes of Hyperbolic 3-Manifolds
24th Workshop in Geometric Topology, Calvin College, June 28, 2007
From playlist Ian Agol: 24th Workshop in Geometric Topology
Ian Agol University of California, Berkeley; Distinguished Visiting Professor, School of Mathematics October 12, 2015 http://www.math.ias.edu/calendar/event/89554/1444672800/1444676400 I'll review recent progress on properties of 3-manifold groups, especially following from geometric pr
From playlist Members Seminar
Genevieve Walsh: Incoherence of free-by-free and surface-by-freegroups
CIRM VIRTUAL EVENT Recorded during the meeting"Virtual Geometric Group Theory conference " the May 29, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM
From playlist Virtual Conference
NonLERFness of groups of certain mixed 3-manifolds and arithmetic hyperbolic n-manifolds - Sun
Geometric Structures on 3-manifolds Topic: NonLERFness of groups of certain mixed 3-manifolds and arithmetic hyperbolic nn-manifolds Speaker: Hongbin Sun Affiliation: University of California, Berkeley Date: Tuesday, May 3 I will show that the groups of mixed 3-manifolds containing a
From playlist Mathematics