Topological group

Definition of a Topological Space

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space

From playlist Topology

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

Topology: Topological Spaces

This video is about topological spaces and some of their basic properties.

From playlist Basics: Topology

Topological Spaces: Introduction & Axioms

The first video in a new series on topological spaces and manifolds.

From playlist Topology & Manifolds

Algebraic topology: Calculating the fundamental group

This lecture is part of an online course on algebraic topology. We calculate the fundamental group of several spaces, such as a ficure 8, or the complement of a circle in R^3, or the group GL3(R). For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EF

From playlist Algebraic topology

Definition of a group Lesson 24

In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el

From playlist Abstract algebra

AlgTopReview4: Free abelian groups and non-commutative groups

Free abelian groups play an important role in algebraic topology. These are groups modelled on the additive group of integers Z, and their theory is analogous to the theory of vector spaces. We state the Fundamental Theorem of Finitely Generated Commutative Groups, which says that any such

From playlist Algebraic Topology

GT2. Definition of Subgroup

Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-

From playlist Abstract Algebra

Symmetric Groups (Abstract Algebra)

Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in

From playlist Abstract Algebra

Classical and Digital Topological Groups

A research talk presented at the Fairfield University Mathematics Research Seminar, October 6, 2022. Should be accessible to a general mathematics audience, combining ideas from topology, graph theory, and abstract algebra. The paper is by me and Dae Woong Lee, available here: https://arx

From playlist Research & conference talks

CTNT 2022 - An Introduction to Galois Representations (Lecture 2) - by Alvaro Lozano-Robledo

This video is part of a mini-course on "An Introduction to Galois Representations" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2022 - An Introduction to Galois Representations (by Alvaro Lozano-Robledo)

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

Lie Groups and Lie Algebras: Lesson 38 - Preparation for the concept of a Universal Covering Group

Lie Groups and Lie Algebras: Lesson 38 - Preparation for the Universal Covering Group concept In this lesson we examine another amazing connection between the algebraic properties of the Lie groups with topological properties. We will lay the foundation to understand how discrete invaria

From playlist Lie Groups and Lie Algebras

CTNT 2020 - Infinite Galois Theory (by Keith Conrad) - Lecture 3

The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2020 - Infinite Galois Theory (by Keith Conrad)

Lie Groups and Lie Algebras: Lesson 36 - Review of continuity and homeomorphisms

Lie Groups and Lie Algebras: Lesson 36 - Review of continuity and homeomorphisms This is a review lesson regarding the topological definition of continuity, homeomorphism, and topological properties. This is important because the Fundamental group of a topological space is a topological

From playlist Lie Groups and Lie Algebras

Lie Groups and Lie Algebras: Lesson 34 -Introduction to Homotopy

Lie Groups and Lie Algebras: Introduction to Homotopy In order to proceed with Gilmore's study of Lie groups and Lie algebras we now need a concept from algebraic topology. That concept is the notion of homotopy and the Fundamental Group of a topological space. In this lecture we provide

From playlist Lie Groups and Lie Algebras

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

Geometric Representation of Structured Extensions in Ergodic Theory - Henrik Kreidler

Special Year Research Seminar Topic: Geometric Representation of Structured Extensions in Ergodic Theory Speaker: Henrik Kreidler Affiliation: Bergische Universität Wuppertal Date: March 14, 2023 The Mackey-Zimmer representation theorem is a key structural result from ergodic theory: Eve

From playlist Mathematics

Group Theory: The Center of a Group G is a Subgroup of G Proof

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Group Theory: The Center of a Group G is a Subgroup of G Proof

From playlist Abstract Algebra

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