Invariants of pseudogroup actions: Homological methods and Finiteness theorem

Details Invariants of pseudogroup actions: Homological methods and Finiteness theorem Invariants of pseudogroup actions: Homological methods and Finiteness theorem

2005-11-29

arxiv.org/abs/math/0511711v2

Mathematics

Differential Geometry

v2: some remarks and references addeed

Scientific paper

We study the equivalence problem of submanifolds with respect to a transitive pseudogroup action. The corresponding differential invariants are determined via formal theory and lead to the notions of k-variants and k-covariants, even in the case of non-integrable pseudogroup. Their calculation is based on the cohomological machinery: We introduce a complex for covariants, define their cohomology and prove the finiteness theorem. This implies the well-known Lie-Tresse theorem about differential invariants. We also generalize this theorem to the case of pseudogroup action on differential equations.

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