Points and curves in the Monster tower / / Richard Montgomery, Michail Zhitomirskii

• Record Nr.: UNINA9910827647103321
• Autore: Montgomery R (Richard), <1956->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2009; ©2009
• ISBN: 1-4704-0570-9
• Descrizione fisica: 1 online resource (137 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 203, Number 956
• Classificazione: SI 130
• Disciplina: 516.3/6
• Soggetti: Jet bundles (Mathematics); Blowing up (Algebraic geometry); Pfaffian systems; Singularities (Mathematics)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 203, Number 956 (end of volume)."
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: ""Contents""; ""Abstract""; ""Preface""; ""Chapter 1. Introduction""; ""1.1. The Monster construction""; ""1.2. Coordinates and the contact case""; ""1.3. Symmetries. Equivalence of points of the Monster""; ""1.4. Prolonging symmetries""; ""1.5. The basic theorem""; ""1.6. The Monster and Goursat distributions""; ""1.7. Our approach""; ""1.8. Proof of the basic theorem""; ""1.9. Plan of the paper""; ""Acknowledgements""; ""Chapter 2. Prolongations of integral curves. Regular, vertical, and critical curves and points ""; ""2.1. From Monster curves to Legendrian curves""; ""2.2. Prolonging curves""""2.3. Projections and prolongations of local symmetries""; ""2.4. Proof of Theorem 2.2""; ""2.5. From curves to points""; ""2.6. Non-singular points""; ""2.7. Critical curves""; ""2.8. Critical and regular directions and points""; ""2.9. Regular integral curves""; ""2.10. Regularization theorem""; ""2.11. An equivalent definition of a non-singular point""; ""2.12. Vertical and tangency directions and points""; ""Chapter 3. RVT classes. RVT codes of plane curves. RVT and Puiseux""; ""3.1. Definition of RVT classes""; ""3.2. Two more definitions of a non-singular point""""3.3. Types of RVT classes. Regular and entirely critical prolongations""; ""3.4. ; Classification problem: reduction to regular RVT classes""; ""3.5. RVT classes as subsets of PkR2 ""; ""3.6. Why tangency points?""; ""3.7. RVT code of plane curves""; ""3.8. RVT code and Puiseux characteristic""; ""Chapter 4. Monsterization and Legendrization. Reduction theorems""; ""4.1. Definitions and basic properties""; ""4.2. Explicit calculation of the legendrization of RVT classes""; ""4.3. From points to Legendrian curves""; ""4.4. Simplest classification results""""4.5. On the implications and shortfalls of Theorems 4.14 and 4.15""; ""4.6. From points to Legendrian curve jets. The jet-identification number ""; ""4.7. The parameterization number""; ""4.8. Evaluating the jet-identification number""; ""4.9. Proof of Proposition 4.44""; ""4.10. From Theorem B to Theorem 4.40""; ""4.11. Proof that critical points do not have a jet-identification number""; ""4.12. Proof of Proposition 4.26""; ""4.13. Conclusions. Things to come""; ""Chapter 5. Reduction algorithm. Examples of classification results""; ""5.1. Algorithm for calculating the Legendrization and the parameterization number""""5.2. Reduction algorithm for the equivalence problem""; ""5.3. Reduction algorithm for the classification problem""; ""5.4. Classes of small codimension consisting of a finite number of orbits""; ""5.5. Classification of tower-simple points""; ""5.6. Classes of high codimension consisting of one or two orbits""; ""5.7. Further examples of classification results; Moduli""; ""Chapter 6. Determination of simple points""; ""6.1. Tower-simple and stage-simple points""; ""6.2. Determination theorems""; ""6.3. Explicit description of stage-simple RVT classes""