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

Dr Trefor Bazett via YouTube

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This introductory course develops the fundamental group using homotopy equivalence and multiplication of loops. It computes fundamental groups for several familiar spaces and applies the concept to prove Brouwer’s Fixed Point Theorem.

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.

Taught by

Dr. Trefor Bazett

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