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Moscow Mathematical Journal

Volume 19, Issue 4, October–December 2019  pp. 761–788.

Poincaré Function for Moduli of Differential-Geometric Structures

Authors:  Boris Kruglikov
Author institution:(1) Department of Mathematics and Statistics, UiT the Arctic University of Norway, Tromsø 90-37, Norway


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.

2010 Math. Subj. Class. 53A55, 22F05, 58H05; 16W22, 13A50.

Keywords: Differential Invariants, Invariant Derivations, conformal metric structure, Hilbert polynomial, Poincaré function.

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