Joseph Krasil'shchik's lectures on the linear differential operators over commutative algebras and geometry of jet spaces: Difference between revisions
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#Representative objects: jets and differential forms. | #Representative objects: jets and differential forms. | ||
#Frölicher-Nijenhuis brackets and related cohomologies. Algebraic model of Hamiltonian formalism. | #Frölicher-Nijenhuis brackets and related cohomologies. Algebraic model of Hamiltonian formalism. | ||
#Frölicher-Nijenhuis brackets and related cohomologies. Algebraic model of nonlinear differential equations. | |||
#Geometric realization. Relation between the category of vector bundle over a manifold and the category of projective modules over a commutative ring. | |||
#Jets of locally trivial bundle over smooth manifolds. The Cartan distribution. | |||
[[Category:Lectures|Krasil'shchik]] | [[Category:Lectures|Krasil'shchik]] | ||
Revision as of 17:38, 3 July 2015
Autumn 2015
Syllabus
- Category and functors (introduction).
- Linear differential operators with values in modules. Main properties.
- Derivations.
- Representative objects: jets and differential forms.
- Frölicher-Nijenhuis brackets and related cohomologies. Algebraic model of Hamiltonian formalism.
- Frölicher-Nijenhuis brackets and related cohomologies. Algebraic model of nonlinear differential equations.
- Geometric realization. Relation between the category of vector bundle over a manifold and the category of projective modules over a commutative ring.
- Jets of locally trivial bundle over smooth manifolds. The Cartan distribution.