Chain (algebraic topology)

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Related lectures (32)

Page 3 of 4

Homomorphisms and Projective Resolutions

Covers homomorphisms, projective modules, and resolutions in chain complexes.

Nerves and Geometric Realization

Covers the explicit computations of nerves of categories and geometric realisations of simplicial sets.

Acyclic Models: Cup Product and Cohomology

Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.

Homotopy Theory in Care Complexes

Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.

Long Exact Sequence of Ext-Modules

Covers the construction of long exact sequences of Ext-modules and provides illustrative examples.

Model Categories: Properties and Structures

Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.

A Lemma: Introduction to Homology Groups

Introduces the concept of homology groups and focuses on a lemma about free abelian groups.

Algebra: Chain Complexes

Explores chain complexes, abelian groups, homomorphisms, homology groups, and free abelian groups.

Chain Maps: Homotopy Invariance

Covers chain maps, homotopy invariance, homology groups, and induced homomorphisms between cycles and boundaries.

Universal Coefficient Theorems

Delves into the universal coefficient theorems in homological algebra, showcasing their practical application in computing homology and cohomology groups.