Integration on manifolds | Algebraic topology

Chain (algebraic topology)

In algebraic topology, a k-chainis a formal linear combination of the k-cells in a cell complex. In simplicial complexes (respectively, cubical complexes), k-chains are combinations of k-simplices (respectively, k-cubes), but not necessarily connected. Chains are used in homology; the elements of a homology group are equivalence classes of chains. (Wikipedia).

Chain (algebraic topology)
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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

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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

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An introduction to homology (cont.) | Algebraic Topology | NJ Wildberger

Here we carry on our introduction to homology, focussing on a particularly simple space, basically a graph and various modifications to it. We discuss cycles, boundaries, and homology as a quotient of cycles mod boundaries, one such group for each dimension. The framework is commutative g

From playlist Algebraic Topology

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Topology 1.4 : Product Topology Introduction

In this video, I define the product topology, and introduce the general cartesian product. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet

From playlist Topology

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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

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Topology 1.5 : Order Topology

In this video, I introduce the order topology and prove that it is Hausdorff. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet

From playlist Topology

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Chain Network - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

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AlgTopReview3: More on commutative groups---isomorphisms, homomorphisms, cosets and quotient groups

We present more information on commutative groups and the fundamental structure theorem that every such group is isomorphic to a direct sum of cyclic groups Z_n. We discuss the notions of isomorphism, homomorphism, cosets of a subgroup, and the quotient of a group by a subgroup. *********

From playlist Algebraic Topology

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String topology coproduct: geometric and algebraic aspects - Manuel Rivera

Princeton/IAS Symplectic Geometry Seminar Topic: String topology coproduct: geometric and algebraic aspects Speaker: Manuel Rivera Affiliation: University of Miami Date: May 11, 2017 For more info, please visit http://video.ias.edu

From playlist Mathematics

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Lie Algebras and Homotopy Theory - Jacob Lurie

Members' Seminar Topic: Lie Algebras and Homotopy Theory Speaker: Jacob Lurie Affiliation: Professor, School of Mathematics Date: November 11, 2019 For more video please visit http://video.ias.edu

From playlist Mathematics

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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

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Sheel Ganatra: The Floer theory of a cotangent bundle, the string topology of the base and...

Find other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies,

From playlist Jean-Morlet Chair - Lalonde/Teleman

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André Henriques: "Various things acted on by fusion categories"

Actions of Tensor Categories on C*-algebras 2021 "Various things acted on by fusion categories" André Henriques - University of Oxford Abstract: Besides von Neumann algebras and C*-algebras, there exist a couple of other mathematical object for which can be acted upon by fusion categorie

From playlist Actions of Tensor Categories on C*-algebras 2021

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CDH methods in K-theory and Hochschild homology - Charles Weibel

Charles Weibel Rutgers University; Member, School of Mathematics November 11, 2013 This is intended to be a survey talk, accessible to a general mathematical audience. The cdh topology was created by Voevodsky to extend motivic cohomology from smooth varieties to singular varieties, assumi

From playlist Mathematics

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Model Categories by Rekha Santhanam

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)

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algebraic geometry 14 Dimension

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the dimension of a topological space, algebraic set, or ring.

From playlist Algebraic geometry I: Varieties

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Charles Weibel: K-theory of algebraic varieties (Lecture 1)

The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Charles Weibel: K theory of algebraic varieties Abstract: Lecture 1 will present definitions for the Waldhausen K-theory of rings, varieties, additive and exact categories, and dg c

From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"

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Sam Fisher: Fibring of RFRS groups

Sam Fisher, University of Oxford Title: Fibring of RFRS groups A group $G$ is said to algrebraically fibre if it admits an epimorphism to $\mathbb{Z}$ with finitely generated kernel. The motivation for this definition comes from a result of Stallings, which states that if $G$ is the fundam

From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

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Karen Vogtmann, Lecture I - 10 February 2015

Karen Vogtmann (U. of Warwick, UK and Cornell University, USA) - Lecture I http://www.crm.sns.it/course/4037/ Automorphism groups of free groups bear similarities to both lattices in Lie groups and to surface mapping class groups. In this minicourse we will explore the cohomology of thes

From playlist Algebraic topology, geometric and combinatorial group theory - 2015

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Minimal Models by Somnath Basu

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)

Related pages

CW complex | Order theory | Homology (mathematics) | Singular homology | Chain complex | Differential geometry | Exterior derivative | Simplicial complex | Cubical complex | Stokes' theorem | Path (topology) | Algebraic topology