Introduction to the fundamental group

A leisurely introduction to the idea of homotopy, including a sketch proof that the fundamental group of the circle is the integers. This is aimed at second year undergrads embarking on projects in geometry/topology who need to quickly learn the basic idea of the fundamental group, so the focus is on developing intuition and explaining the definitions.

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Intro to the Fundamental Group // Algebraic Topology with @TomRocksMaths
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Intro to the Fundamental Group // Algebraic Topology with @TomRocksMaths

Algebraic topology: Fundamental group
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Algebraic topology: Fundamental group

The fundamental group | Algebraic Topology 24 | NJ Wildberger
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The fundamental group | Algebraic Topology 24 | NJ Wildberger

Dirac's belt trick, Topology, and Spin ½ particles
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Dirac's belt trick, Topology, and Spin ½ particles

Conceptualizing the Christoffel Symbols: An Adventure in Curvilinear Coordinates
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Conceptualizing the Christoffel Symbols: An Adventure in Curvilinear Coordinates

What is Group Theory? — Group Theory Ep. 1
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What is Group Theory? — Group Theory Ep. 1

Watch this if everything feels too much (gentle comfort for tired women)
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Watch this if everything feels too much (gentle comfort for tired women)

We're 99.9% sure this pattern is true, but no one can prove it
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We're 99.9% sure this pattern is true, but no one can prove it

Algebraic Topology 2: Introduction to Fundamental Group
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Algebraic Topology 2: Introduction to Fundamental Group

Algebraic Topology 1.3 : Path Homotopy and Product (Animation Included)
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Algebraic Topology 1.3 : Path Homotopy and Product (Animation Included)

An introduction to homology | Algebraic Topology 30 | NJ Wildberger
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An introduction to homology | Algebraic Topology 30 | NJ Wildberger

An Intuitive Introduction to Motivic Homotopy Theory - Vladimir Voevodsky [2002]
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An Intuitive Introduction to Motivic Homotopy Theory - Vladimir Voevodsky [2002]

The second homotopy group of the sphere: π₂(S²) in classical and digital topology
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The second homotopy group of the sphere: π₂(S²) in classical and digital topology

This open problem taught me what topology is
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This open problem taught me what topology is

What is algebraic topology?
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What is algebraic topology?

The fundamental group of the circle
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The fundamental group of the circle

Group theory, abstraction, and the 196,883-dimensional monster
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Group theory, abstraction, and the 196,883-dimensional monster

The Mathematical Problem with Music, and How to Solve It
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The Mathematical Problem with Music, and How to Solve It

Algebraic Topology 3: Fundamental Group is a Group!
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Algebraic Topology 3: Fundamental Group is a Group!

Lie Algebras and Homotopy Theory - Jacob Lurie
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Lie Algebras and Homotopy Theory - Jacob Lurie