Cohomology of the infinite-order jet space
G.Giachetta, L.Mangiarotti, G.Sardanashvily
TL;DR
This paper computes the De Rham cohomology and related cohomologies of the differential algebra on the infinite-order jet space of a smooth fibre bundle, advancing the understanding of its geometric structure.
Contribution
It provides explicit calculations of cohomology groups for the differential algebra on infinite-order jet spaces, a novel contribution in differential geometry.
Findings
De Rham cohomology of the jet space is explicitly calculated.
Cohomology groups related to $d_V$ and $d_H$ are determined.
Results enhance understanding of the geometric and topological properties of jet spaces.
Abstract
De Rham cohomology, - and -cohomology of the differential algebra of locally pull-back exterior forms on the infinite-order jet manifold of a smooth fibre bundle are calculated.
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Taxonomy
TopicsNonlinear Waves and Solitons · Geometric Analysis and Curvature Flows · Geometry and complex manifolds