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Subgroup Decomposition in $\mathsf {Out}(F_n)$
About this Title
Michael Handel, Lehman College, CUNY and Lee Mosher, Rutgers University, Newark
Publication: Memoirs of the American Mathematical Society
Publication Year:
2020; Volume 264, Number 1280
ISBNs: 978-1-4704-4113-5 (print); 978-1-4704-5802-7 (online)
DOI: https://doi.org/10.1090/memo/1280
Published electronically: April 20, 2020
MSC: Primary 20F28; Secondary 20E05, 20F65, 57M07
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. Ping-pong on geodesic lines
- 15. Proof of Theorem C
- 16. A filling lemma
Abstract
In this work we 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 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.- Y. Algom-Kfir and L. Mosher, Lectures on mapping class groups, Lectures by Lee Mosher at MSRI, Fall 2007. Notes by Yael Algom-Kfir. Available at https://www.math.utah.edu/$\sim$yael/MCG/.
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