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Algebraic domains
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Classroom Contents
Poincaré-Reeb Graphs of Real Algebraic Domains
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- 1 Intro
- 2 Setting and goals
- 3 Algebraic domains
- 4 Overview
- 5 The Poincaré-Reeb graph
- 6 The asymptotic Poincaré-Reeb tree
- 7 Reformulation
- 8 The polar curve
- 9 Choosing a generic projection
- 10 The generic asymptotic Poincaré-Reeb tree
- 11 The discriminant locus
- 12 Genericity hypotheses
- 13 1. Positive asymptotic snake
- 14 2. Arnold's snake (one variable)
- 15 Idea of the proof
- 16 The construction
- 17 Separable permutations
- 18 Nonseparable permutation - example
- 19 Separable tree
- 20 Passing to the univariate case
- 21 The contact tree
- 22 Answer in the univariate case
- 23 Construction of the desired bivariate polynomial f
- 24 Flip-Flop Algorithm
- 25 Vertical planes
- 26 The topological critical set
- 27 Domain of finite type
- 28 Vertical equivalence
- 29 Complete invariant
- 30 Invariance of the Euler characteristic
- 31 Strategy of the proof
- 32 Non-compact Poincaré-Reeb graphs
