Algebraic topology

Algebraic topology: Introduction

This lecture is part of an online course on algebraic topology. This is an introductory lecture, where we give a quick overview of some of the invariants of algebraic topology (homotopy groups, homology groups, K theory, and cobordism). The book "algebraic topology" by Allen Hatcher men

From playlist Algebraic topology

Homotopy animation

An interesting homotopy (in fact, an ambient isotopy) of two surfaces.

From playlist Algebraic Topology

AlgTopReview: An informal introduction to abstract algebra

This is a review lecture on some aspects of abstract algebra useful for algebraic topology. It provides some background on fields, rings and vector spaces for those of you who have not studied these objects before, and perhaps gives an overview for those of you who have. Our treatment is

From playlist Algebraic Topology

Algebraic Topology - 5.1 - Mappings Spaces and the Compact Open Topology

We define the compact open topology on mapping spaces.

From playlist Algebraic Topology

AlgTop1: One-dimensional objects

This is the first lecture of this beginner's course in Algebraic Topology (after the Introduction). In it we introduce the two basic one-dimensional objects: the line and circle. The latter has quite a few different manifestations: as a usual Euclidean circle, as the projective line of one

From playlist Algebraic Topology: a beginner's course - N J Wildberger

AlgTop22: Knots and surfaces I

From playlist Algebraic Topology: a beginner's course - N J Wildberger

Algebraic topology: Fundamental group of a knot

This lecture is part of an online course on algebraic topology. We calculate the fundamental group of (the complement of) a knot, and give a couple of examples. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52yxQGxQoxwOtjIEtxE2BWx

From playlist Algebraic topology

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

Algebraic Topology - 12.1 - Fibrations and Cofibrations

From playlist Algebraic Topology

Teena Gerhardt - 1/3 Algebraic K-theory and Trace Methods

Algebraic K-theory is an invariant of rings and ring spectra which illustrates a fascinating interplay between algebra and topology. Defined using topological tools, this invariant has important applications to algebraic geometry, number theory, and geometric topology. One fruitful approac

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

Proving Brouwer's Fixed Point Theorem | Infinite Series

Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi There is a proof for Brouwer's Fixed Point Theorem that uses a bridge - or portal - between geometry and algebra. Tweet at us! @pbsinfinite Facebook: facebook.com/pbs

From playlist An Infinite Playlist

Even spaces and motivic resolutions - Michael Hopkins

Vladimir Voevodsky Memorial Conference Topic: Even spaces and motivic resolutions Speaker: Michael Hopkins Affiliation: Harvard University Date: September 13, 2018 For more video please visit http://video.ias.edu

From playlist Mathematics

Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group

Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group We are finally in position to understand the nature of the Universal Covering Group and its connection to all the Lie groups which share a single Lie algebra. This is a critical lecture! In this lecture we simply state

From playlist Lie Groups and Lie Algebras

Duality in Algebraic Geometry by Suresh Nayak

PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics

From playlist Dualities in Topology and Algebra (Online)

The rising sea: Grothendieck on simplicity and generality - Colin McLarty [2003]

Slides for this talk: https://drive.google.com/file/d/1yDmqhdcKo6-YpDpRdHh2hvuNirZVbcKr/view?usp=sharing Notes for this talk: https://drive.google.com/open?id=1p45B3Hh8WPRhdhQAd0Wq0MvmY0JYSnmc The History of Algebra in the Nineteenth and Twentieth Centuries April 21 - 25, 2003 Colin Mc

From playlist Mathematics

A search for an algebraic equivalence analogue of motivic theories - Eric Friedlander

Vladimir Voevodsky Memorial Conference Topic: A search for an algebraic equivalence analogue of motivic theories Speaker: Eric Friedlander Affiliation: University of Southern California Date: September 13, 2018 For more video please visit http://video.ias.edu

From playlist Mathematics

Teena Gerhardt - 3/3 Algebraic K-theory and Trace Methods

Algebraic K-theory is an invariant of rings and ring spectra which illustrates a fascinating interplay between algebra and topology. Defined using topological tools, this invariant has important applications to algebraic geometry, number theory, and geometric topology. One fruitful approac

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

Epic Math Book Speed Run

In this video I do a speed run of some of my math books. I go through math books covering algebra, trigonometry, calculus, advanced calculus, real analysis, abstract algebra, differential geometry, set theory, discrete math, finite math, graph theory, combinatorics, number theory, galois t

From playlist Book Reviews

Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined

Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined In this lecture we define a "continuous groups" and show the connection between the algebraic properties of a group with topological properties. Please consider supporting this channel via Patreon: https://www.patreon.co

From playlist Lie Groups and Lie Algebras

Coffee Cup Donut

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

From playlist Algebraic Topology