دانلود کتاب Mirzakhani’s Curve Counting and Geodesic Currents

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Preface
Acknowledgments
Contents
Notation
1 Introduction
Some Things that the Reader Will Not Find in This Book
What the Reader Will Find Here
A Comment on the Way This Book Is Written
2 Read Me
Curves, Multicurves, and Arcs
Intersection Number
Geodesic Representatives
Random Geodesics. Or Length Versus Intersections
Space of Geodesics
Geodesics Projecting into a Fixed Compact Set
Laminations
Hausdorff Limits
Mapping Class Group
Shortening Curves
3 Geodesic Currents
Definition and Examples
Curves as Currents
Weighted Multicurves
Measured Laminations
The Space of Geodesic Currents
Interesting Subsets of C(Σ)
Intersection Form
Characterization of Measured Laminations
Filling Currents
The Mapping Class Group Action
Mapping Class Group Action on the Set of Filling Currents
Comments (The Liouville Current)
4 Train Tracks
Train Tracks as Smoothly Embedded Complexes
Almost Geodesic Train Tracks
Band Complexes and Train Tracks
Curves and Laminations Carried by Train Tracks
Weights and Recurrence
Switch Equations
Thurston Measure
First Counting Result
Masur\'s Ergodicity Theorem
An Example: The Case of the Once Punctured Torus
Comments
Piecewise Linear Structure
Symplectic Structure
Weil–Petersson Volume Form
Other Interesting Measures on ML(S)
5 Radallas
Terminology
The Game of Cars
Almost Geodesic Radallas
Finding Almost Geodesic Radallas
Generic Curves
Comments: Expected Angle of Self-Intersection
6 Subconvergence of Measures
Idea of the Proof of Theorem 6.1
Local Map
Global Map
New Measures
Comments
7 Approximating the Thurston Measure
Dribbling
Radallas Carrying the Curves in Θσ0
Reducing to a Linear Algebra Problem
Proof of Proposition 7.2
Comments
8 The Main Theorem
Notation and the Constants
The Theorem
The Fundamental Domain
The Meat
The Not Ker-Invariant Case
Comments
9 Counting Curves
Main Curve Counting Theorem
Frequencies and Relative Frequencies
Functions on the Space of Currents
10 Counting Square-Tiled Surfaces
Square-Tiled Surfaces
Recovering Square-Tiled Surface Structures from Multicurves
Square-Tiled Surfaces of Given Type
Counting
Comments
11 Statistics of Simple Curves
Credit to Kasra
Hard Data
A Formula for c(α0) for Simple Curves
Punctured Spheres
Separating Curves in Closed Surfaces
Non-Separating Curves in Closed Surfaces
Combinatorial Computation
Changing Weights
Comments
12 Smörgåsbord
Random Pants Decompositions
Lattice Point Counting in Teichmüller Space
Genericty of pseudo-Anosov Elements
A Radon Measures
Point-Set Topology
Weak-*-Topology
Sequential Compactness
B Computing Thurston Volumes
Punctured Spheres
Separating Curves in Closed Surfaces
Non-separating Curves in Closed Surfaces
References
Index