Invariants of pseudogroup actions: Homological methods and Finiteness theorem
Abstract
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 l-variants and
l-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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