Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Computing homology groups | Algebraic Topology | NJ Wildberger
The definition of the homology groups H_n(X) of a space X, say a simplicial complex, is quite abstract: we consider the complex of abelian groups generated by vertices, edges, 2-dim faces etc, then define boundary maps between them, then take the quotient of kernels mod boundaries at each
From playlist Algebraic Topology
Isomorphisms in abstract algebra
In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4
From playlist Abstract algebra
Kernel of a group homomorphism
In this video I introduce the definition of a kernel of a group homomorphism. It is simply the set of all elements in a group that map to the identity element in a second group under the homomorphism. The video also contain the proofs to show that the kernel is a normal subgroup.
From playlist Abstract algebra
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
BM8.3. Mappings 3: Composition and Inverse Mappings
Basic Methods: We define composition of mappings and draw parallels to multiplication of real numbers. Items include associativity, identity, and commutativity. Consideration of multiplicative inverses leads to the definition of an inverse mapping, and we give conditions for its existenc
From playlist Math Major Basics
Homotopy elements in the homotopy group π₂(S²) ≅ ℤ. Roman Gassmann and Tabea Méndez suggested some improvements to my original ideas.
From playlist Algebraic Topology
In this tutorial I cross the bridge between a standard algebraic function and products sets, as well as mappings. I show the three types of mappings, namely injective (one-to-one), surjective (onto), and their combination, a bijection.
From playlist Abstract algebra
Jonathan Belcher: Bridge cohomology-a generalization of Hochschild and cyclic cohomologies
Talk by Jonathan Belcher in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-... on August 12, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
EDIT: At 8:35, should use q instead of pi. Abstract Algebra: We define homomorphism between groups and draw connections to normal subgroups and quotient groups. Precisely the kernel of a homomorphism is a normal subgroup, and we can associate a surjective homomorphism to every normal
From playlist Abstract Algebra
Symplectic implosion - Lisa Jeffrey
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Symplectic implosion Speaker: Lisa Jeffrey Affiliation: University of Toronto Date: January 14, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Persistence and Triangulation in Lagrangian Topology - Paul Biran
IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: Persistence and Triangulation in Lagrangian Topology Speaker: Paul Biran Affiliation: Eidgenössische Technische Hochschule (ETH) Zürich Date: November 20, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Duality for Rabinowitz-Floer homology - Alex Oancea
IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: Duality for Rabinowitz-Floer homology Speaker: Alex Oancea Affiliation: Institut de Mathématiques de Jussieu-Paris Rive Gauche Date: May 27, 2020 For more video please visit http://video.ias.edu
From playlist PU/IAS Symplectic Geometry Seminar
Duality In Higher Categories II by Pranav Pandit
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)
Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, ... 4
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Basic Homotopy Theory by Samik 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)
Spatial refinements and Khovanov homology – Robert Lipshitz & Sucharit Sarkar – ICM2018
Topology Invited Lecture 6.11 Spatial refinements and Khovanov homology Robert Lipshitz & Sucharit Sarkar Abstract: We review the construction and context of a stable homotopy refinement of Khovanov homology. © International Congress of Mathematicians – ICM www.icm2018.org Os direi
From playlist Topology
Spanier Whitehead Duality by Samik 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)
The Kernel of a Group Homomorphism – Abstract Algebra
The kernel of a group homomorphism measures how far off it is from being one-to-one (an injection). Suppose you have a group homomorphism f:G → H. The kernel is the set of all elements in G which map to the identity element in H. It is a subgroup in G and it depends on f. Different ho
From playlist Abstract Algebra