In topology, puncturing a manifold is removing a finite set of points from that manifold. The set of points can be small as a single point. In this case, the manifold is known as once-punctured. With the removal of a second point, it becomes twice-punctured, and so on. Examples of punctured manifolds include the open disk (which is a sphere with a single puncture), the cylinder (which is a sphere with two punctures), and the Möbius strip (which is a projective plane with a single puncture). (Wikipedia).
Applied topology 3: A punctured torus is homotopy equivalent to a figure eight
Applied topology 3: A punctured torus is homotopy equivalent to a figure eight Abstract: We give an impromptu explanation of why a punctured torus (i.e., a torus with a single point removed) is homotopy equivalent to a figure eight (i.e., two circles glued together at a single point). In
From playlist Applied Topology - Henry Adams - 2021
Topology (What is a Topology?)
What is a Topology? Here is an introduction to one of the main areas in mathematics - Topology. #topology Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, b
From playlist Topology
To a topologist, a coffee cup and a donut are the same thing.
From playlist Algebraic Topology
I define closed sets, an important notion in topology and analysis. It is defined in terms of limit points, and has a priori nothing to do with open sets. Yet I show the important result that a set is closed if and only if its complement is open. More topology videos can be found on my pla
From playlist Topology
In this video, I cover the notion of continuity, as used in topology. The beautiful thing is that this doesn't use epsilon-delta at all, and instead just something purely geometric. Enjoy this topology-adventure! Topology Playlist: https://youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGG
From playlist Topology
Is there a difference between a donut and a cup of coffee? It turns out the answer is no! In this video, we'll define the notion of homeomorphism and see why those two objects are homeomorphic. Enjoy! Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGGBXRMV32
From playlist Topology
Topology 1.3 : Basis for a Topology
In this video, I define what a basis for a topology is. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
Here is one of the most important curves in mathematics. It is an example of a set that is connected, but not path-connected, and is very prominent in topology and analysis. Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGGBXRMV32EKVI Subscribe to my channel
From playlist Topology
Edward Witten: "What's (Relatively) New in Two-Dimensional Gravity”
Green Family Lecture Series 2017 "What's (Relatively) New in Two-Dimensional Gravity” Edward Witten, Institute for Advanced Study Abstract: The talk will be devoted to explaining two relatively recent mathematical developments involving what physicists know as topological gravity in two
From playlist Public Lectures
The Geometry of soap films -- minimal surfaces by Rukmini Dey
PROGRAM : SUMMER SCHOOL FOR WOMEN IN MATHEMATICS AND STATISTICS ORGANIZERS : Siva Athreya and Anita Naolekar DATE : 13 May 2019 to 24 May 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore The summer school is intended for women students studying in first year B.A/B.Sc./B.E./B.Tech.
From playlist Summer School for Women in Mathematics and Statistics 2019
There's a Donut in the Wallpaper: Topology, Symmetry, and Conway's Magic Theorem
Made for the 3Blue1Brown Summer of Math Exploration
From playlist Summer of Math Exposition Youtube Videos
Geometric Langlands and 3d Mirror Symmetry (Lecture 1) by Sam Raskin
Program Quantum Fields, Geometry and Representation Theory 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pandi
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
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
Plastic version: http://shpws.me/HEtj This is joint work with Keenan Crane. I never said it was a good joke.
From playlist 3D printing
Louis Funar : Automorphisms of curve and pants complexes in profinite content
Pants complexes of large surfaces were proved to be vigid by Margalit. We will consider convergence completions of curve and pants complexes and show that some weak four of rigidity holds for the latter. Some key tools come from the geometry of Deligne Mumford compactification of moduli sp
From playlist Topology
Sam Raskin: Tate's thesis in the de Rham setting
SMRI Algebra and Geometry Online 'Tate's thesis in the de Rham setting' Sam Raskin (The University of Texas at Austin) Abstract: This is joint work with Justin Hilburn. We will explain a theorem showing that D-modules on the Tate vector space of Laurent series are equivalent to ind-cohere
From playlist SMRI Algebra and Geometry Online
Sergey Shemyakov: Transcendental Thurston theory for entire functions and compositions
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 23, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audi
From playlist Dynamical Systems and Ordinary Differential Equations
Topology 1.7 : More Examples of Topologies
In this video, I introduce important examples of topologies I didn't get the chance to get to. This includes The discrete and trivial topologies, subspace topology, the lower-bound and K topologies on the reals, the dictionary order, and the line with two origins. I also introduce (again)
From playlist Topology