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portada Descargar ficha PDF Título: Points And Curves In The Monster Tower
Autor: Montgomery Richard/ Zhitomirskii Michail Precio: $910.71
Editorial: American Mathematical Society Año: 2009
Tema: Matematicas, Textos, Teorias Edición:
Sinopsis ISBN: 9780821848180
Cartan introduced the method of prolongation which can be applied either to manifolds with distributions (Pfaffian systems) or integral curves to these distributions. Repeated application of prolongation to the plane endowed with its tangent bundle yields the Monster tower, a sequence of manifolds, each a circle bundle over the previous one, each endowed with a rank 2 distribution. In an earlier paper (2001), the authors proved that the problem of classifying points in the Monster tower up to symmetry is the same as the problem of classifying Goursat distribution flags up to local diffeomorphism. The first level of the Monster tower is a three-dimensional contact manifold and its integral curves are Legendrian curves. The philosophy driving the current work is that all questions regarding the Monster tower (and hence regarding Goursat distribution germs) can be reduced to problems regarding Legendrian curve singularities.

Table of Contents

Introduction
Prolongations of integral curves. Regular, vertical, and critical curves and points
RVT classes. RVT codes of plane curves. RVT and Puiseux
Monsterization and Legendrization. Reduction theorems
Reduction algorithm. Examples of classification results
Determination of simple points
Local coordinate systems on the Monster
Prolongations and directional blow-up. Proof of Theorems A and B
Open questions
Appendix A. Classification of integral Engel curves
Appendix B. Contact classification of Legendrian curves
Appendix C. Critical, singular and rigid curves
Bibliography
Index
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