Concept
Singular homology
Related lectures (69)
Simplicial Homology: Examples
Explores examples of simplicial homology by equipping known topological spaces with delta complex structures.
Homology with coefficients
Covers homology with coefficients, introducing the concept of defining homology groups with respect to arbitrary abelian groups.
EML Spaces and Cohomology
Covers spaces, homology, chain groups, and abelianization in CW complexes and maps.
Cellular Homology: Applications
Delves into applying cellular homology to compute homology groups and Euler characteristic, showcasing its practical implications.
Topology Seminar: Tower Sequences and Homomorphisms
Explores tower sequences, homomorphisms, and their applications in topology, including the computation of homology and the construction of telescopes.
Graded Ring Structure on Cohomology
Explores the associative and commutative properties of the cup product in cohomology, with a focus on graded structures.
A Lemma: Introduction to Homology Groups
Introduces the concept of homology groups and focuses on a lemma about free abelian groups.
Algebraic Kunneth Theorem
Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.
Homotopy theory of chain complexes
Explores the homotopy theory of chain complexes, focusing on defining cylinder objects and left homotopy.
Cohomology Groups: Hopf Formula
Explores the Hopf formula in cohomology groups, emphasizing the 4-term exact sequence and its implications.