Lie groups | 3-manifolds | Kleinian groups | Automorphic forms | Discrete groups
In mathematics, a Kleinian group is a discrete subgroup of the group of orientation-preserving isometries of hyperbolic 3-space H3. The latter, identifiable with PSL(2, C), is the quotient group of the 2 by 2 complex matrices of determinant 1 by their center, which consists of the identity matrix and its product by −1. PSL(2, C) has a natural representation as orientation-preserving conformal transformations of the Riemann sphere, and as orientation-preserving conformal transformations of the open unit ball B3 in R3. The group of Möbius transformations is also related as the non-orientation-preserving isometry group of H3, PGL(2, C). So, a Kleinian group can be regarded as a discrete subgroup acting on one of these spaces. (Wikipedia).
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The Klein Four-Group is the smallest noncyclic abelian group. Every proper subgroup is cyclic. We look at the the multiplication in the Klein Four-Group and find all of it's subgroups.
From playlist Abstract Algebra
G. Walsh - Boundaries of Kleinian groups
We study the problem of classifying Kleinian groups via the topology of their limit sets. In particular, we are interested in one-ended convex-cocompact Kleinian groups where each piece in the JSJ decomposition is a free group, and we describe interesting examples in this situation. In ce
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
Definition of a group Lesson 24
In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el
From playlist Abstract algebra
Jacob explains the fundamental concepts in group theory of what groups and subgroups are, and highlights a few examples of groups you may already know. Abelian groups are named in honor of Niels Henrik Abel (https://en.wikipedia.org/wiki/Niels_Henrik_Abel), who pioneered the subject of
From playlist Basics: Group Theory
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
There is no better way of understanding product groups than working through and example. In this video we look at the product group of the cyclic group with two elements and itself. The final result is isomorphic to what we call the Klein 4 group.
From playlist Abstract algebra
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
Profinite rigidity – Alan Reid – ICM2018
Topology Invited Lecture 6.7 Profinite rigidity Alan Reid Abstract: We survey recent work on profinite rigidity of residually finite groups. © International Congress of Mathematicians – ICM www.icm2018.org Os direitos sobre todo o material deste canal pertencem ao Instituto de Mat
From playlist Topology
Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-
From playlist Abstract Algebra
Boundaries of Kleinian groups - Genevieve Walsh
Genevieve Walsh, Tufts October 7, 2015 http://www.math.ias.edu/wgso3m/agenda Monday, October 5, 2015 - 08:00 to Friday, October 9, 2015 - 12:00 This workshop is part of the topical program "Geometric Structures on 3-Manifolds" which will take place during the 2015-2016 academic year at t
From playlist Workshop on Geometric Structures on 3-Manifolds
Cannon–Thurston maps – Mahan Mj – ICM2018
Geometry Invited Lecture 5.9 Cannon–Thurston maps Mahan Mj Abstract: We give an overview of the theory of Cannon–Thurston maps which forms one of the links between the complex analytic and hyperbolic geometric study of Kleinian groups. We also briefly sketch connections to hyperbolic sub
From playlist Geometry
Hyperbolic groups, Cannon-Thurston maps, and hydra - Timothy Riley
Timothy Riley Cornell University; Member, School of Mathematics November 17, 2014 Groups are Gromov-hyperbolic when all geodesic triangles in their Cayley graphs are close to being tripods. Despite being tree-like in this manner, they can harbour extreme wildness in their subgroups. I wil
From playlist Mathematics
Algebraic Ending Laminations and Quasiconvexity by Mahan Mj
Surface Group Representations and Geometric Structures DATE: 27 November 2017 to 30 November 2017 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The focus of this discussion meeting will be geometric aspects of the representation spaces of surface groups into semi-simple Lie groups. Classi
From playlist Surface Group Representations and Geometric Structures
Hausdorff dimension of Kleinian group uniformization of Riemann surface... - Yong Hou
Topic: Hausdorff dimension of Kleinian group uniformization of Riemann surface and conformal rigidity Speaker: Yong Hou Date:Tuesday, November 24 For this talk I'll discuss uniformization of Riemann surfaces via Kleinian groups. In particular question of conformability by Hasudorff dimens
From playlist Mathematics
Ahlfors-Bers 2014 "Quasi-isometric rigidity of the class of convex-cocompact Kleinian groups"
Peter Haïssinsky (Toulouse): The talk will be devoted to discussing background and ingredients for the proof of the following theorem: a finitely generated group quasi-isometric to a convex-cocompact Kleinian group contains a finite index subgroup isomorphic to a convex-cocompact Kleinian
From playlist The Ahlfors-Bers Colloquium 2014 at Yale
What is a Group? | Abstract Algebra
Welcome to group theory! In today's lesson we'll be going over the definition of a group. We'll see the four group axioms in action with some examples, and some non-examples as well which violate the axioms and are thus not groups. In a fundamental way, groups are structures built from s
From playlist Abstract Algebra
Center of a group in abstract algebra
After the previous video where we saw that two of the elements in the dihedral group in six elements commute with all the elements in the group, we finally get to define the center of a group. The center of a group is a subgroup and in this video we also go through the proof to show this.
From playlist Abstract algebra
Indra's Pearls: A Mathematical Adventure
Public Lecture by Caroline Series (University of Warwick) Here are the weblinks to the sites mentioned in the video Jos Leys Mathematical Imagery Beautiful mathematical graphics including Kleinian limit sets. http://www.josleys.com Open source software to make Kleinian limit sets. http
From playlist Public Lectures