This is a glossary of properties and concepts in algebraic topology in mathematics. See also: glossary of topology, list of algebraic topology topics, glossary of category theory, glossary of differential geometry and topology, Timeline of manifolds. * Convention: Throughout the article, I denotes the unit interval, Sn the n-sphere and Dn the n-disk. Also, throughout the article, spaces are assumed to be reasonable; this can be taken to mean for example, a space is a CW complex or compactly generated weakly Hausdorff space. Similarly, no attempt is made to be definitive about the definition of a spectrum. A simplicial set is not thought of as a space; i.e., we generally distinguish between simplicial sets and their geometric realizations. * Inclusion criterion: As there is no in Wikipedia right now, this glossary also includes a few concepts in homological algebra (e.g., chain homotopy); some concepts in geometric topology and differential topology are also fair game. On the other hand, the items that appear in glossary of topology are generally omitted. Abstract homotopy theory and motivic homotopy theory are also outside the scope. Glossary of category theory covers (or will cover) concepts in theory of model categories. (Wikipedia).
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
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
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
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
Bad Math Glossary, or Soviet Propaganda?
A review of "The Algebra Tutor, Algebra 1 and Algebra 2, Volume 1". A textbook/workbook by Willie L. Thomas. It has a great propaganda-esque cover design, and a very finicky glossary to put it nicely. #mathbook #math 00:00 Rest of the Review 19:33 The Bad Glossary 23:00 End Buy a copy o
From playlist The Math Library
Claire Amiot: Cluster algebras and categorification - Part 1
Abstract: In this course I will first introduce cluster algebras associated with a triangulated surface. I will then focus on representation of quivers, and show the strong link between cluster combinatorics and representation theory. The aim will be to explain additive categorification of
From playlist Combinatorics
Gallai-Edmonds Percolation by Kedar Damle
DISCUSSION MEETING : STATISTICAL PHYSICS OF COMPLEX SYSTEMS ORGANIZERS : Sumedha (NISER, India), Abhishek Dhar (ICTS-TIFR, India), Satya Majumdar (University of Paris-Saclay, France), R Rajesh (IMSc, India), Sanjib Sabhapandit (RRI, India) and Tridib Sadhu (TIFR, India) DATE : 19 December
From playlist Statistical Physics of Complex Systems - 2022
AlgTop2: Homeomorphism and the group structure on a circle
This is the first video of the second lecture in this beginner's course on Algebraic Topology. We give the basic definition of homeomorphism between two topological spaces, and explain why the line and circle are not homeomorphic. Then we introduce the group structure on a circle, or in f
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Antonio Marcianò : Kac-Moody instantons in space-time forma as an alternative solution to the ...
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 31, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
To a topologist, a coffee cup and a donut are the same thing.
From playlist Algebraic Topology
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
Representations of finite groups of Lie type (Lecture 1) by Dipendra Prasad
PROGRAM : GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fun
From playlist Group Algebras, Representations And Computation
Algebraic geometry 44: Survey of curves
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives an informal survey of complex curves of small genus.
From playlist Algebraic geometry I: Varieties
How Many Holes Does a Human Have?
Support Vsauce, your brain, Alzheimer's research, and other YouTube educators by joining THE CURIOSITY BOX: a seasonal delivery of viral science toys made by Vsauce! A portion of all proceeds goes to Alzheimer's research and our Inquisitive Fellowship, a program that gives money and resour
From playlist Knowledge
My favorite LaTeX packages for writing beautiful math documents
Get started with LaTeX using Overleaf: ►https://www.overleaf.com?utm_source=yt&utm_medium=link&utm_campaign=im22tb Overleaf is an excellent cloud-based LaTeX editor that makes learning and using LaTeX just so much easier. My thanks to Overleaf for sponsoring this video! ►Check out my LaT
From playlist LaTeX Tutorials
Worldwide Differential Calculus Reference App
The demo of our new apps on the iPad & iPhone!
From playlist Center of Math ARCHIVES: Watch the good, the bad, and the ugly
The Study of Pre-modern Hebrew Philosophical and Scientific Terminology as a new Chapte... - Various
Near Eastern Studies and Digital Scholarship@IAS joint lecture Topic: The Study of Pre-modern Hebrew Philosophical and Scientific Terminology as a new Chapter in the Intellectual History of Europe and the Islamicate World: PESHAT in Context. Speakers (Affiliation): Giuseppe Veltri (Unive
From playlist Historical Studies
Algebraic Topology - 5.1 - Mappings Spaces and the Compact Open Topology
We define the compact open topology on mapping spaces.
From playlist Algebraic Topology
A short video on terms such as Vector Space, SubSpace, Span, Basis, Dimension, Rank, NullSpace, Col space, Row Space, Range, Kernel,..
From playlist Tutorial 4