YoVDO

Fundamental Group of Surfaces - Multiplication and Properties

Offered By: Insights into Mathematics via YouTube

Tags

Algebraic Topology Courses Group Theory Courses Mathematical Proofs Courses Topology Courses Fundamental Groups Courses Torus Courses

Course Description

Overview

Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only!
Delve deeper into the fundamental group of a surface in this 35-minute lecture on Algebraic Topology. Prove that the multiplication of equivalence classes or types of loops from a base point forms a group in the algebraic sense. Explore the fundamental group of the torus and the projective plane. Learn about multiplication, identity, constant loops, inverses, and associativity through detailed proofs and picture examples. Conclude with a discussion on the projective plane and a problem to describe the fundamental group of a given space. Suitable for beginners in Algebraic Topology, this lecture is part of a course given by N J Wildberger of UNSW.

Syllabus

More on the fundamental group
Multiplication
Theorem
Proof -Identity & constant loop
Inverses
Associativity
picture examples
Projective plane
Problem 26. Describe...


Taught by

Insights into Mathematics

Related Courses

Introduction to Algebraic Topology (Part-I)
Indian Institute of Technology Bombay via Swayam
Introduction to Algebraic Topology (Part-II)
NPTEL via Swayam
Intro to the Fundamental Group - Algebraic Topology with Tom Rocks Maths
Dr Trefor Bazett via YouTube
The Fundamental Group - Algebraic Topology
Insights into Mathematics via YouTube
Lie Algebras and Homotopy Theory - Jacob Lurie
Institute for Advanced Study via YouTube