INVARIANTS OF PSEUDOGROUP ACTIONS: HOMOLOGICAL METHODS AND FINITENESS THEOREM
- 1 September 2006
- journal article
- Published by World Scientific Pub Co Pte Ltd in International Journal of Geometric Methods in Modern Physics
- Vol. 3 (5), 1131-1165
- https://doi.org/10.1142/s0219887806001478
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.Keywords
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