A Monster Tower Approach to Goursat Multi-flags
نویسندگان
چکیده
We consider the problem of classifying the orbits within a tower of fibrations with P-fibers that generalize the Monster Tower due to Montgomery and Zhitomirskii. The action on the tower is given by prolongations of diffeomorphism germs of 3-space. As a corollary we give the first steps towards the problem of classifying Goursat 2-flags of small length. In short, we classify the orbits within the first four levels of the Monster Tower and show that there is a total of 34 orbits in the fourth level of the tower.
منابع مشابه
Geometric Approach to Goursat Flags
A Goursat flag is a chain Ds ⊂ Ds−1 ⊂ D1 ⊂ D0 = TM of subbundles of the tangent bundle TM such that corank Di = i and Di−1 is generated by the vector fields in Di and their Lie brackets. Engel, Goursat, and Cartan studied these flags and established a normal form for them, valid at generic points of M . Recently Kumpera, Ruiz and Mormul discovered that Goursat flags can have singularities, and ...
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