Motivation from dynamics – a brief sketch

Pilgrim K.M.

Table of contents :
1.1 Motivation from dynamics–a brief sketch……Page 1
1.2 Thurston’s Characterization and Rigidity Theorem. Standard definitions……Page 2
1.3.2 An obstructed mating……Page 6
1.3.3 An obstructed expanding Thurston map……Page 8
1.3.4 A subdivision rule……Page 11
1.4 Summary of this work……Page 12
1.5.1 Enumeration……Page 14
1.5.2 Combinations and decompositions……Page 17
1.5.3 Parameter space……Page 20
1.5.4 Combinations via quasiconformal surgery……Page 22
1.5.5 From p.f. to geometrically finite and beyond……Page 23
1.6 Analogy with three-manifolds……Page 24
1.7.1 Geometric Galois theory……Page 27
1.7.2 Gromov hyperbolic spaces and interesting groups……Page 28
1.8 Discussion of combinatorial subtleties……Page 29
1.8.1 Overview of decomposition and combination……Page 30
1.8.2 Embellishments. Technically convenient assumption…….Page 31
1.8.3 Invariant multicurves for embellished map of spheres. Thurston linear map…….Page 32
1.9 Tameness assumptions……Page 33