Algebraic topology

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Related lectures (30)

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Cohomology: Abelian Cochains

Introduces cohomology, focusing on abelian cochains and their correspondence with singular cochains.

Tangent Spaces in Algebraic Geometry

Explores derivations and the Zariski tangent space in algebraic geometry, emphasizing their importance and practical applications.

Natural Transformations: Functor L

Explores natural transformations in category theory with a focus on the functor L and its algebraic properties.

Topology: Free Groups and Their Properties

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

Linear Representations: Basics and Examples

Covers linear representations, isomorphism, G modules, and classification of representations of C star and C plus.

Lie Algebra Homomorphisms

Explores the association of Lie algebras to algebraic groups and homomorphisms.

Exponential Maps: Properties and Applications in Lie Groups

Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.

Further Directions: Algebraic Groups

Explores various directions for studying algebraic groups and offers references for further exploration.

Cohomology Representations: Lecture 14.1

Covers the concept of cohomology representations and the implications of reduced suspension operations on spaces.

Homotopy Theory: Cylinders and Path Objects

Covers cylinders, path objects, and homotopy in model categories.