Intro to the Fundamental Group - Algebraic Topology with Tom Rocks Maths

Explore the fascinating world of algebraic topology in this 44-minute video lecture focusing on the fundamental group. Learn about the topologist's perspective on the alphabet, the algebra of loops, and homotopy equivalence. Discover how to compute the fundamental group for various spaces, including the plane, sphere, circle, and torus. Gain insights into the power of the fundamental group through a proof of Brouwer's Fixed Point Theorem. Delve into the intersection of algebra and topology, understanding how concrete mathematical operations apply to continuously deformable spaces.

Syllabus

What is Algebraic Topology?.
The alphabet to a topologist.
The algebra of loops about a ring.
Defining Homotopy Equivalence.
The Fundamental Group .
Fundamental Group of R^2.
Fundamental Group of a Sphere.
Fundamental Group of a Circle.
Fundamental Group of a Torus.
Proof of Brouwer's Fixed Point Theorem.