Pinch and Fold: Fundamentals of Group Theory

Related lectures (31)

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Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Covers the construction of a telescope using cylinders on circles and the calculation of fundamental groups for various spaces.

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

Covers the construction and universal properties of pushouts in group theory.

Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.

Discusses the classification of surfaces and their fundamental groups using the Seifert-van Kampen theorem and polygonal presentations.

Delves into symmetries in physics, covering group theory, perturbation, and quantification.

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.