Exterior Algebra with Differential Forms on Manifolds

The Cartan algebra of exterior differential forms as a supermanifold: morphisms and manifolds associated with them

A supermanifold, Mm/n, can be caracterired by its smooth superfunctions which constitute an algebra A (Leites, Kostant). We associate canonically ~a Ia Gelfand, certain fibred manifolds on which the automorphisms (the Jordan automorphisms) of A actas diffeomorphisms. For example, the kernelsof all homomorphisms from the algebra of superfunctions onto the Grassmann algebra of dimension n form na...

The Application of Exterior Differential Forms in Variational Problems on Manifolds

The exterior differential forms are introduced to solve the complicated variational problems on 2-dimensional manifolds in R3. It is easy to generalize this method to the higher dimensional manifolds. [email protected] [email protected]

The Harmonic Operator for Exterior Differential Forms.

Tracking Invariant Manifolds without Differential Forms

A frequently studied problem of geometric singular perturbation theory consists in establishing the presence of trajectories of certain types (homoclinic, heteroclinic, satisfying given boundary conditions, etc.) approximating singular ones for the unperturbed problem. A useful tool for this problem has been established in Jones et al. [2] and called “Exchange Lemma” by the authors. It resemble...

Graph Braid Groups Exterior Face Algebras and Differential Forms

I am a geometric group theorist. Geometric group theory is a highly interdisciplinary field focusing on the study of groups via their actions on geometric spaces. Geometric group theory uses the tools and approaches of algebraic topology, commutative algebra, semigroup theory, hyperbolic geometry, geometric analysis, combinatorics, computational group theory, computational complexity theory, lo...