Topology

Puncture (topology)

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).

Video thumbnail

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

Video thumbnail

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

Video thumbnail

Coffee Cup Donut

To a topologist, a coffee cup and a donut are the same thing.

From playlist Algebraic Topology

Video thumbnail

What is a closed set ?

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

Video thumbnail

Continuity in 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

Video thumbnail

What is a Homeomorphism

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

Video thumbnail

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

Video thumbnail

Topologist Sine Curve

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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)

Video thumbnail

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

Video thumbnail

Topology joke

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Related pages

Manifold | Finite set | Projective plane | Disk (mathematics) | Sphere | Topology | Möbius strip