 | Handel M. Axes in outer space / M.Handel, L.Mosher. - Providence: American Mathematical Society, 2011. - v, 104 p. - (Memoirs of the American Mathematical Society; vol.213, N 1004). - Bibliogr.: p.103-104. - ISBN 978-0-8218-6927-7; ISSN 0065-9266
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Chapter 1 Introduction ......................................... 1
1.1 Characterizations of the axis bundle ....................... 2
1.2 The main theorems .......................................... 6
1.3 A question of Vogtmann ..................................... 7
1.4 Contents and proofs ........................................ 7
1.5 Problems and questions .................................... 10
Chapter 2 Preliminaries ....................................... 15
2.1 Outer space and outer automorphisms ....................... 15
2.2 Paths, circuits and edge paths ............................ 20
2.3 Folds ..................................................... 22
2.4 Train track maps .......................................... 24
2.5 The attracting tree T+ .................................... 28
2.6 Geodesic laminations in trees and marked graphs ........... 33
2.7 The expanding lamination Λ_ ............................... 35
2.8 Relating Λ_ to T_ and to T+ ............................... 38
Chapter 3 The ideal Whitehead graph ........................... 41
3.1 Definition and structure of the ideal Whitehead graph ..... 42
3.2 Asymptotic leaves and the ideal Whitehead graph ........... 44
3.3 T+ and the ideal Whitehead graph .......................... 45
3.4 An example of an ideal Whitehead graph .................... 46
Chapter 4 Cutting and pasting local stable Whitehead graphs ... 49
4.1 Pasting local stable Whitehead graphs ..................... 49
4.2 Cutting local stable Whitehead graphs ..................... 51
4.3 The finest local decomposition ............................ 52
Chapter 5 Weak train tracks ................................... 55
5.1 Local decomposition of the ideal Whitehead graph .......... 56
5.2 Folding up to a weak train track .......................... 57
5.3 Comparing train tracks to weak train tracks ............... 59
5.4 Rigidity and irrigidity of Λ_ isometries .................. 62
5.5 Examples of exceptional weak train tracks ................. 65
Chapter 6 Topology of the axis bundle ......................... 69
6.1 Continuity properties of the normalized axis bundle ....... 69
6.2 The Gromov topology on weak train tracks .................. 71
6.3 Properness of the length map .............................. 74
6.4 Applying Skora's method to the Properness Theorem 6.1 ..... 77
6.5 Remarks on stable train tracks ............................ 84
Chapter 7 Fold lines .......................................... 87
7.1 Examples of fold paths .................................... 87
7.2 Characterizing fold lines ................................. 93
7.3 Direct limits of fold rays ................................ 94
7.4 Legal laminations of split rays ........................... 97
7.5 Weak train tracks on fold lines .......................... 101
Bibliography .................................................. 103
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