Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


cohomology

Cohomology of the Lie Algebra of Vector Fields on Some One-dimensional Orbifold

I. M. Gelfand and D. B. Fuchs have proved that the cohomology algebra of the Lie algebra of vector fields on the unit circle is isomorphic to the tensor product of the polynomial ring with one generator of degree two and the exterior algebra with one generator of degree three. In the present paper the cohomology of the Lie algebra of vector fields on the one-dimensional orbifold S1/Z2 are studied. S1/Z2 is the orbit space under the Z2 group action on the unit circle by reflection in the Ox axis.

Cohomology of Lie algebra of vector fields on S1/Z2

 In the present paper we calculate the diagonal cohomology of Lie algebra of vector fields on S1/Z2 with coefficients in the space of smooth functions and 1-forms, one-dimensional and two-dimensional cohomology with coefficients in R. 

Foliation on Distribution with Finslerian Metric

A distribution D with a admissible Finsler metric is defined on a smooth manifold X. Let F be a foliation on X. On the distribution of D as on a smooth manifold foliation F corresponds to the foliation TF. Using this foliation and connection over distribution we define analog exterior derivative. Exterior differential forms is applied to a special form.