Subgroup decomposition in out(Fn):
In this work we develop a decomposition theory for subgroups of which generalizes the decomposition theory for individual elements of found in work of Bestvina, Feighn, and Handel, and which is analogous to the decomposition theory for subgroups of mapping class groups found in work of Ivanov.
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
March 2020
|
| Series: | Memoirs of the American Mathematical Society
volume 264, number 1280 (third of 6 numbers) |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | In this work we develop a decomposition theory for subgroups of which generalizes the decomposition theory for individual elements of found in work of Bestvina, Feighn, and Handel, and which is analogous to the decomposition theory for subgroups of mapping class groups found in work of Ivanov. |
| Item Description: | Literaturverzeichnis: Seite 271-273 |
| Physical Description: | vii, 276 Seiten Illustrationen |
| ISBN: | 9781470441135 |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 264, number 1280 (third of 6 numbers) | |
| 500 | |a Literaturverzeichnis: Seite 271-273 | ||
| 520 | |a In this work we develop a decomposition theory for subgroups of which generalizes the decomposition theory for individual elements of found in work of Bestvina, Feighn, and Handel, and which is analogous to the decomposition theory for subgroups of mapping class groups found in work of Ivanov. | ||
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Record in the Search Index
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| adam_text | American Mathematical Society
Number 1280
Subgroup Decomposition in Out(Fn)
Michael Handel
Lee Mosher
ULB Darmstadt
iniiiiiiiiii
20396490
March 2020 • Volume 264 • Number 1280 (third of 6 numbers)
Universitäts- und
Landesbibliothek
Darmstadt
Ä
0 AMERICAN
A KA mathematical
■,mVLJ SOCIETY
Contents
Introduction to Subgroup Decomposition 1
The main theorem, slightly simplified 2
Rotationless versus IAn(Z/3) (Part II) 3
The main theorem, full version 4
The relative Kolchin theorem for Out(F„) (Part II) 6
Geometric models (Part I) 8
Vertex group systems (Part I) 9
Weak attraction theory (Part III) 9
Relatively irreducible subgroups (Part IV) 11
Part I Geometric Models 15
Introduction to Part I 17
Chapter 1 Preliminaries: Decomposing outer automorphisms 23
1 1 Fn and its subgroups, marked graphs, and lines 23
1 2 Subgroup systems carrying lines and other things 31
1 3 Attracting laminations 35
1 4 Principal automorphisms and rotationless outer automorphisms 36
1 5 Relative train track maps and CTs 39
1 6 Properties of Attracting Laminations 54
Chapter 2 Geometric EG strata and geometric laminations 65
2 1 Defining and characterizing geometric strata 65
2 2 Complementary subgraph and peripheral splitting 78
2 3 The laminations of a geometric stratum 81
2 4 Geometricity is an invariant of a dual lamination pair 91
2 5 Stabilizing its complement also stabilizes the surface 92
2 6 Preserving the free boundary circles 95
Chapter 3 Vertex groups and vertex group systems 103
3 1 Vertex group systems 103
3 2 Geometric models and vertex group systems 105
Part II A relative Kolchin theorem 109
Introduction to Part II 111
Chapter 1 Statements of the main results 113
Chapter 2 Preliminaries 117
Ui
CONTENTS
iv
2 1 Polynomial growth relative to a free factor system 117
2 2 Fn-trees 118
2 3 One-edge extensions: free factor systems versus graphs 119
2 4 Asymptotic data: attracting laminations, eigenrays, and twistors 120
2 5 Complete splittings rel Gr 125
2 6 Fixed subgroup systems 126
Chapter 3 An outline of the relative Kolchin theorem 129
Chapter 4 IAn(Z/3) periodic conjugacy classes 133
4 1 Reduction to: Fn is filled by the 0-periodic conjugacy classes 134
4 2 Each CT /: G - G representing p is geometric/linear/fixed 134
4 3 The case that U£(0) fills 135
4 4 The case that UC(8) does not fill: a one-edge extension 139
4 5 The case that U£(ö) does not fill: conclusion 141
Chapter 5 IA„(Z/3) periodic free factors 147
5 1 Reduction to one-edge extensions: Proposition 5 1 147
5 2 Relative Nielsen classes and the path set T 149
5 3 Proof that IAn(Z/3) periodic free factors are fixed: Theorem 3 1 157
Chapter 6 Limit Trees 161
6 1 Iteration of growers 162
6 2 Iteration of nongrowers 164
Chapter 7 Carrying asymptotic data: Proposition 3 4 169
7 1 Carrying eigenrays 169
7 2 The exponential growth digraph for twistors 170
7 3 Bouncing sequences 175
Chapter 8 Finding Nielsen pairs: Proposition 3 7 179
Part III Weak Attraction Theory 189
Introduction to Part III 191
Chapter 1 The nonattracting subgroup system 195
1 1 The nonattracting subgroup system Ana(Aj) 196
1 2 Applications and properties of the nonattracting subgroup system 201
1 3 Weak convergence and malnormal subgroup systems 203
Chapter 2 Nonattracted lines 205
2 1 Characterizing nonattracted lines: Theorem G 205
2 2 Concatenating special nonattracted lines 208
2 3 Proof of Theorem H 212
2 4 Nonattracted lines of EG height: the nongeometric case 213
2 5 Nonattracted lines of EG height: the geometric case 216
2 6 General nonattracted lines: Proof of Theorem G 229
Part IV Relatively irreducible subgroups 235
Introduction to Part IV 237
CONTENTS
Chapter 1 Ping-pong on geodesic lines 241
1 1 Finding attracting laminations by the “three over one” criterion 241
1 2 The ping-pong argument 242
Chapter 2 Proof of Theorem C 249
2 1 Reduction to Theorem I 249
2 2 Constructing a conjugator 250
2 3 Driving down -4na(Aj) 252
2 4 Driving up Fsupp( F, Aj): Proof of Theorem I 256
2 5 Relatively geometric irreducible subgroups: Theorem J 261
Chapter 3 A filling lemma 267
Bibliography 271
|
| adam_txt |
American Mathematical Society
Number 1280
Subgroup Decomposition in Out(Fn)
Michael Handel
Lee Mosher
ULB Darmstadt
iniiiiiiiiii
20396490
March 2020 • Volume 264 • Number 1280 (third of 6 numbers)
Universitäts- und
Landesbibliothek
Darmstadt
Ä
0 AMERICAN
A KA \ mathematical
■,mVLJ SOCIETY
Contents
Introduction to Subgroup Decomposition 1
The main theorem, slightly simplified 2
Rotationless versus IAn(Z/3) (Part II) 3
The main theorem, full version 4
The relative Kolchin theorem for Out(F„) (Part II) 6
Geometric models (Part I) 8
Vertex group systems (Part I) 9
Weak attraction theory (Part III) 9
Relatively irreducible subgroups (Part IV) 11
Part I Geometric Models 15
Introduction to Part I 17
Chapter 1 Preliminaries: Decomposing outer automorphisms 23
1 1 Fn and its subgroups, marked graphs, and lines 23
1 2 Subgroup systems carrying lines and other things 31
1 3 Attracting laminations 35
1 4 Principal automorphisms and rotationless outer automorphisms 36
1 5 Relative train track maps and CTs 39
1 6 Properties of Attracting Laminations 54
Chapter 2 Geometric EG strata and geometric laminations 65
2 1 Defining and characterizing geometric strata 65
2 2 Complementary subgraph and peripheral splitting 78
2 3 The laminations of a geometric stratum 81
2 4 Geometricity is an invariant of a dual lamination pair 91
2 5 Stabilizing its complement also stabilizes the surface 92
2 6 Preserving the free boundary circles 95
Chapter 3 Vertex groups and vertex group systems 103
3 1 Vertex group systems 103
3 2 Geometric models and vertex group systems 105
Part II A relative Kolchin theorem 109
Introduction to Part II 111
Chapter 1 Statements of the main results 113
Chapter 2 Preliminaries 117
Ui
CONTENTS
iv
2 1 Polynomial growth relative to a free factor system 117
2 2 Fn-trees 118
2 3 One-edge extensions: free factor systems versus graphs 119
2 4 Asymptotic data: attracting laminations, eigenrays, and twistors 120
2 5 Complete splittings rel Gr 125
2 6 Fixed subgroup systems 126
Chapter 3 An outline of the relative Kolchin theorem 129
Chapter 4 IAn(Z/3) periodic conjugacy classes 133
4 1 Reduction to: Fn is filled by the 0-periodic conjugacy classes 134
4 2 Each CT /: G - G representing p is geometric/linear/fixed 134
4 3 The case that U£(0) fills 135
4 4 The case that UC(8) does not fill: a one-edge extension 139
4 5 The case that U£(ö) does not fill: conclusion 141
Chapter 5 IA„(Z/3) periodic free factors 147
5 1 Reduction to one-edge extensions: Proposition 5 1 147
5 2 Relative Nielsen classes and the path set T 149
5 3 Proof that IAn(Z/3) periodic free factors are fixed: Theorem 3 1 157
Chapter 6 Limit Trees 161
6 1 Iteration of growers 162
6 2 Iteration of nongrowers 164
Chapter 7 Carrying asymptotic data: Proposition 3 4 169
7 1 Carrying eigenrays 169
7 2 The exponential growth digraph for twistors 170
7 3 Bouncing sequences 175
Chapter 8 Finding Nielsen pairs: Proposition 3 7 179
Part III Weak Attraction Theory 189
Introduction to Part III 191
Chapter 1 The nonattracting subgroup system 195
1 1 The nonattracting subgroup system Ana(Aj) 196
1 2 Applications and properties of the nonattracting subgroup system 201
1 3 Weak convergence and malnormal subgroup systems 203
Chapter 2 Nonattracted lines 205
2 1 Characterizing nonattracted lines: Theorem G 205
2 2 Concatenating special nonattracted lines 208
2 3 Proof of Theorem H 212
2 4 Nonattracted lines of EG height: the nongeometric case 213
2 5 Nonattracted lines of EG height: the geometric case 216
2 6 General nonattracted lines: Proof of Theorem G 229
Part IV Relatively irreducible subgroups 235
Introduction to Part IV 237
CONTENTS
Chapter 1 Ping-pong on geodesic lines 241
1 1 Finding attracting laminations by the “three over one” criterion 241
1 2 The ping-pong argument 242
Chapter 2 Proof of Theorem C 249
2 1 Reduction to Theorem I 249
2 2 Constructing a conjugator 250
2 3 Driving down -4na(Aj) 252
2 4 Driving up Fsupp( F, Aj): Proof of Theorem I 256
2 5 Relatively geometric irreducible subgroups: Theorem J 261
Chapter 3 A filling lemma 267
Bibliography 271 |
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| illustrated | Illustrated |
| index_date | 2024-07-03T15:04:04Z |
| indexdate | 2024-07-10T08:54:59Z |
| institution | BVB |
| isbn | 9781470441135 |
| language | English |
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| physical | vii, 276 Seiten Illustrationen |
| publishDate | 2020 |
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| publisher | American Mathematical Society |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Handel, Michael 1949- (DE-588)173977391 aut Subgroup decomposition in out(Fn) Michael Handel, Lee Mosher Providence, RI American Mathematical Society March 2020 vii, 276 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 264, number 1280 (third of 6 numbers) Literaturverzeichnis: Seite 271-273 In this work we develop a decomposition theory for subgroups of which generalizes the decomposition theory for individual elements of found in work of Bestvina, Feighn, and Handel, and which is analogous to the decomposition theory for subgroups of mapping class groups found in work of Ivanov. Geometrische Gruppentheorie (DE-588)4651615-3 gnd rswk-swf Geometrische Gruppentheorie (DE-588)4651615-3 s DE-604 Mosher, Lee 1957- (DE-588)1015095364 aut Memoirs of the American Mathematical Society volume 264, number 1280 (third of 6 numbers) (DE-604)BV008000141 1280 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032237767&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Handel, Michael 1949- Mosher, Lee 1957- Subgroup decomposition in out(Fn) Memoirs of the American Mathematical Society Geometrische Gruppentheorie (DE-588)4651615-3 gnd |
| subject_GND | (DE-588)4651615-3 |
| title | Subgroup decomposition in out(Fn) |
| title_auth | Subgroup decomposition in out(Fn) |
| title_exact_search | Subgroup decomposition in out(Fn) |
| title_exact_search_txtP | Subgroup decomposition in out(Fn) |
| title_full | Subgroup decomposition in out(Fn) Michael Handel, Lee Mosher |
| title_fullStr | Subgroup decomposition in out(Fn) Michael Handel, Lee Mosher |
| title_full_unstemmed | Subgroup decomposition in out(Fn) Michael Handel, Lee Mosher |
| title_short | Subgroup decomposition in out(Fn) |
| title_sort | subgroup decomposition in out fn |
| topic | Geometrische Gruppentheorie (DE-588)4651615-3 gnd |
| topic_facet | Geometrische Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032237767&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT handelmichael subgroupdecompositioninoutfn AT mosherlee subgroupdecompositioninoutfn |