Odd variational sequences on finite order jet spaces
Jaroslav \v{S}tef\'anek
Abstract: For a fibered manifold $\pi:Y \to X$ with possibly non-orientable
base we introduce an ``odd variational sequence" of sheaves over the (finite)
$r$-jet prolongation $J^rY$. We give a description of cohomology spaces of
this odd variational sequence by means of cohomology spaces of the odd de Rham
sequence over $Y$. With help of double cover of $X$ we describe the relation
between the spaces of odd base differential forms and ordinary differential
forms over $Y$, which allows us to express the cohomology of the odd
variational sequence in terms of ordinary de Rham cohomology.
Key words: Jet prolongation of a fibered manifold, differential form,
odd base differential form, double cover of a manifold, sheaf.
MS classification: 58E99, 57N65, 57R22.