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Subgroup Decomposition in $\mathrm{Out}(F_n)$
Softcover ISBN:  9781470441135 
Product Code:  MEMO/264/1280 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $51.00 
eBook ISBN:  9781470458027 
Product Code:  MEMO/264/1280.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $51.00 
Softcover ISBN:  9781470441135 
eBook: ISBN:  9781470458027 
Product Code:  MEMO/264/1280.B 
List Price:  $170.00 $127.50 
MAA Member Price:  $153.00 $114.75 
AMS Member Price:  $102.00 $76.50 
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Subgroup Decomposition in $\mathrm{Out}(F_n)$
Softcover ISBN:  9781470441135 
Product Code:  MEMO/264/1280 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $51.00 
eBook ISBN:  9781470458027 
Product Code:  MEMO/264/1280.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $51.00 
Softcover ISBN:  9781470441135 
eBook ISBN:  9781470458027 
Product Code:  MEMO/264/1280.B 
List Price:  $170.00 $127.50 
MAA Member Price:  $153.00 $114.75 
AMS Member Price:  $102.00 $76.50 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 264; 2020; 276 ppMSC: Primary 20; Secondary 57
In this work the authors develop a decomposition theory for subgroups of \(\mathsf{Out}(F_n)\) which generalizes the decomposition theory for individual elements of \(\mathsf{Out}(F_n)\) found in the work of Bestvina, Feighn, and Handel, and which is analogous to the decomposition theory for subgroups of mapping class groups found in the work of Ivanov.

Table of Contents

Chapters

Introduction to Subgroup Decomposition

1. Geometric Models

Introduction to Part I

1. Preliminaries: Decomposing outer automorphisms

2. Geometric EG strata and geometric laminations

3. Vertex groups and vertex group systems

2. A relative Kolchin theorem

Introduction to Part II

4. Statements of the main results

5. Preliminaries

6. An outline of the relative Kolchin theorem

7. $IA_n(\mathbb {Z}/3)$ periodic conjugacy classes

8. $IA_n(\mathbb {Z}/3)$ periodic free factors

9. Limit Trees

10. Carrying asymptotic data: Proposition

11. Finding Nielsen pairs: Proposition

3. Weak Attraction Theory

Introduction to Part III

12. The nonattracting subgroup system

13. Nonattracted lines

4. Relatively irreducible subgroups

Introduction to Part IV

14. Pingpong on geodesic lines

15. Proof of Theorem C

16. A filling lemma


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Volume: 264; 2020; 276 pp
MSC: Primary 20; Secondary 57
In this work the authors develop a decomposition theory for subgroups of \(\mathsf{Out}(F_n)\) which generalizes the decomposition theory for individual elements of \(\mathsf{Out}(F_n)\) found in the work of Bestvina, Feighn, and Handel, and which is analogous to the decomposition theory for subgroups of mapping class groups found in the work of Ivanov.

Chapters

Introduction to Subgroup Decomposition

1. Geometric Models

Introduction to Part I

1. Preliminaries: Decomposing outer automorphisms

2. Geometric EG strata and geometric laminations

3. Vertex groups and vertex group systems

2. A relative Kolchin theorem

Introduction to Part II

4. Statements of the main results

5. Preliminaries

6. An outline of the relative Kolchin theorem

7. $IA_n(\mathbb {Z}/3)$ periodic conjugacy classes

8. $IA_n(\mathbb {Z}/3)$ periodic free factors

9. Limit Trees

10. Carrying asymptotic data: Proposition

11. Finding Nielsen pairs: Proposition

3. Weak Attraction Theory

Introduction to Part III

12. The nonattracting subgroup system

13. Nonattracted lines

4. Relatively irreducible subgroups

Introduction to Part IV

14. Pingpong on geodesic lines

15. Proof of Theorem C

16. A filling lemma
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