Concept
Betti number
Related lectures (16)
The Topological Künneth Theorem
Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.
Poincare Inequality: Young the Quality on the Night
Covers mathematical estimations and algebraic identities in fully discrete problems.
Universal Coefficient Theorems
Delves into the universal coefficient theorems in homological algebra, showcasing their practical application in computing homology and cohomology groups.
Group Operations and Homomorphisms in Abelian Groups
Explores operations on abelian groups, Homomorphisms, adjoints, and morphisms in group theory.
Singular Homology: First Properties
Covers the first properties of singular homology and the preservation of decomposition and path-connected components in topological spaces.
Simplicial and Singular Homology Equivalence
Demonstrates the equivalence between simplicial and singular homology, proving isomorphisms for finite s-complexes and discussing long exact sequences.
Acyclic Models: Cup Product and Cohomology
Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.
Homology with coefficients
Covers homology with coefficients, introducing the concept of defining homology groups with respect to arbitrary abelian groups.
Representation of Lorentz Fields
Explains the representation of Lorentz fields and the concept of gravitons and gravitinos.
Sobolev Spaces and Continuous Embeddings
Covers Sobolev spaces, continuous embeddings, weak convergence, and Poincare inequalities.