This article is cited in 3 papers

Poincaré function for moduli of differential-geometric structures

Boris Kruglikov

Department of Mathematics and Statistics, UiT the Arctic University of Norway, Tromsø 90-37, Norway

Abstract: The Poincaré function is a compact form of counting moduli in local geometric problems. We discuss its property in relation to V. Arnold's conjecture, and derive this conjecture in the case when the pseudogroup acts algebraically and transitively on the base. Then we survey the known counting results for differential invariants and derive new formulae for several other classification problems in geometry and analysis.

Key words and phrases: Differential Invariants, Invariant Derivations, conformal metric structure, Hilbert polynomial, Poincaré function.

MSC: Primary 53A55, 22F05, 58H05; Secondary 16W22, 13A50

Language: English

DOI: 10.17323/1609-4514-2019-19-4-761-788

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