Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Piotr Mormul
Pages: [1] - [27]
Received Date: January 11, 2013; Revised January 2, 2014
Submitted by:
Goursat distributions - subbundles in the tangent bundles to manifolds having the tower of consecutive Lie squares growing very slowly in ranks, always only by one - possess, from corank 8 onwards, numerical moduli of the local classification up to diffeomorphisms of base manifolds. (Up to corank 7 that classification is finite.) The number of such moduli grows with the corank, i.e., with the length of a tower. Yet there are no other (more involved, e.g., functional) moduli of the local classification. A natural question, asked by Agrachev in the year 2000, is whether those numerical moduli descend to the level of nilpotent approximations: whether they are resistant enough to survive the passing to the nilpotent level. A surprising negative result in this direction was obtained in [21]; it dealt with a Goursat modulus appearing in codimension three, in corank (or length) 8. In the present work, we show that it is likewise – a modulus disappears on the nilpotent level – for the first Goursat modulus found, [19], in codimension two (i.e., in the smallest possible codimension, classification in codimension one, [17], being discrete).
nilpotent approximation, Goursat distribution, numerical invariant.
