Invariants of pseudogroup actions: Homological methods and Finiteness theorem

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Invariants of pseudogroup actions: Homological methods and Finiteness theorem

 

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Title: Invariants of pseudogroup actions: Homological methods and Finiteness theorem
Author: Kruglikov, Boris; Lychagin, Valentin V.
Date: 07-Dec-2005
Type: Working paper; Arbeidsnotat
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.
URI: http://hdl.handle.net/10037/2053


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