Do Moduli of Goursat Distributions Appear on the Level of Nilpotent Approximations?
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It is known that Goursat distributions (subbundles in the tangent bundles having the tower of consecutive Lie squares growing in ranks very slowly, always by one) possess, from corank 8 onwards, numerical moduli of the local classification, in both C∞ and real analytic categories. (Whereas up to corank 7 that classification is discrete, as shown in a series of papers, the last in that series being .)
A natural question, first asked by A.Agrachev in 2000, is whether the moduli of Goursat distributions descend to the level of nilpotent approximations: whether they are stiff enough to survive the passing to the nilpotent level. In the present work we show that it is not the case for the first modulus appearing in corank 8 (and the only one known to-date in that corank).
KeywordsNilpotent approximation Goursat distribution local classification continuous invariant modulus
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