Index

Adjacency of an RVT class, 29

A-singularities, 43,109

Blow-up, 109

Badly parameterized curve, 22

Contact manifold, 1

Critical curve, 17

direction, 20

point, 20

RVT class, 28

Cartan theorem in Monster terms, 3, 17, 28

Darboux theorem in Monster terms, 3

Directional blow-up, 95

Engel theorem in Monster terms, 3

Engel manifold, 3, 119

Equivalent curves in the Monster, 4

points of the Monster, 2

Entirely critical RVT class, 28

Fencing RVT classes, 73

Goursat distribution, 3

Integral curves, 4

Jet-identification number

of a point, 45

of an RVT class, 47

KR coordinates, 85

Legendrian curves, 4, 123

Legendrization, 39

Level of the Monster, 1

Local simplicity, 79

Maps Pc , RVT , 33, 36, 37

Moduli, 69

Monster, 1

Monsterization, 39

Non-singular point, 17, 23, 28

Order of good parameterization, 47

Parameterization number, 48

Projection of a curve, 13

of a symmetry, 15

Prolongation of a curve, 13

of a symmetry, 2, 15

Puiseux characteristic, 35, 113

Regular curve, 20

direction, 20

point, 20

prolongation of a point, 21

prolongation of an RVT class, 28

Rigid curve, 18, 131

RL-contact equivalence, 4, 45

RVT class, 27

code of a point, class, 27

code of a plane curve, 32

Singular point, 17,23,28

Simple point, 5, 71

Stage-simple point, 71

RVT class, 72

Symmetry of the Monster, 2

Singularity class, 26

Singular (abnormal) curves, 18, 131

Tangency direction, 24

point, 25

Tower-simple point, 71

RVT class, 72

Vertical curve, 17

direction, 24

point, 25

Well-parameterized curve, 22

∆i, PiR2,

1

Φk,

πi,j , Φk, Γk ,

Γk,

2, 13,14,15

Leg(P1R2),

16

Leg(p), Leg(Q), 39, 40

ET, EV, Eω, 36

ord(f), 90

P, P(1), 95, 96

137