LEADER 04983nam 2200673 450 001 9910827647103321 005 20170816143319.0 010 $a1-4704-0570-9 035 $a(CKB)3360000000465140 035 $a(EBL)3114050 035 $a(SSID)ssj0000889145 035 $a(PQKBManifestationID)11566331 035 $a(PQKBTitleCode)TC0000889145 035 $a(PQKBWorkID)10867761 035 $a(PQKB)11556690 035 $a(MiAaPQ)EBC3114050 035 $a(RPAM)15950884 035 $a(PPN)19541845X 035 $a(EXLCZ)993360000000465140 100 $a20150415h20092009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPoints and curves in the Monster tower /$fRichard Montgomery, Michail Zhitomirskii 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2009. 210 4$dİ2009 215 $a1 online resource (137 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 203, Number 956 300 $a"Volume 203, Number 956 (end of volume)." 311 $a0-8218-4818-6 320 $aIncludes bibliographical references and index. 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""6.3. Explicit description of stage-simple RVT classes"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 203, Number 956. 606 $aJet bundles (Mathematics) 606 $aBlowing up (Algebraic geometry) 606 $aPfaffian systems 606 $aSingularities (Mathematics) 615 0$aJet bundles (Mathematics) 615 0$aBlowing up (Algebraic geometry) 615 0$aPfaffian systems. 615 0$aSingularities (Mathematics) 676 $a516.3/6 686 $aSI 130$2rvk 700 $aMontgomery$b R$g(Richard),$f1956-$01638681 702 $aZhitomirskii?$b Mikhail 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827647103321 996 $aPoints and curves in the Monster tower$93981262 997 $aUNINA