Concept
Poincaré lemma
Related lectures (25)
Differential Forms Integration
Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.
Meromorphic Functions & Differentials
Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.
Advanced Physics I
Covers advanced physics topics including definitions, rectilinear motion, vectors, and motion in three dimensions.
Homology groups: Quotients
Covers homology groups of quotients, homotopy invariance, and exact sequences.
Harmonic Forms and Riemann Surfaces
Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.
Mathematical Complements: df or δf
Explores mathematical tools for differentials of functions of multiple variables and their practical applications in thermodynamics and real-life scenarios.
Homotopy Invariance: Homology Groups
Explores homotopy invariance and its application to homology groups of quotients, showcasing isomorphism and chain homotopy.
Relative Homology: Homotopy Invariance
Explains relative homology, n-cycles, n-boundaries, and exact sequences of chain complexes.
Induced Homomorphisms
Covers induced homomorphisms, homotopy invariance, and homology groups of quotients.
Chain Maps: Homotopy Invariance
Covers chain maps, homotopy invariance, homology groups, and induced homomorphisms between cycles and boundaries.