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Subgroup Decomposition in Mathrm{Out}(F_{n})
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 ma...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2020.
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| Colección: | Memoirs of the American Mathematical Society Ser.
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| Temas: |
Manifolds and cell complexes {For complex manifolds, see 32Qxx}
> Low-dimensional topology
> Topological methods in group theory.
Group theory and generalizations
> Structure and classification of infinite or finite groups
> Free nonabelian groups.
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| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover
- Title page
- Introduction to Subgroup Decomposition
- The main theorem, slightly simplified
- Rotationless versus \IA_{ }(\Z/3) (\PartTwo)
- The main theorem, full version
- The relative Kolchin theorem for \Out( _{ }) (\PartTwo)
- Geometric models (\PartOne)
- Vertex group systems (\PartOne)
- Weak attraction theory (\PartThree)
- Relatively irreducible subgroups (\PartFour)
- Part I . Geometric Models
- Introduction to \PartOne
- Chapter 1. Preliminaries: Decomposing outer automorphisms
- 1.1. _{ } and its subgroups, marked graphs, and lines
- 1.1.1. The geometry of _{ } and its subgroups.
- 1.1.2. Subgroup systems, free factor systems, and malnormality.
- Malnormal subgroup systems.
- 1.1.3. Restrictions of outer automorphisms.
- 1.1.4. Marked graphs, paths, and circuits.
- 1.1.5. Spaces of paths and lines.
- Rays.
- 1.1.6. The path maps _{#} and _{##}, and bounded cancellation.
- 1.2. Subgroup systems carrying lines and other things
- 1.2.1. Subgroup systems carrying lines, rays, and conjugacy classes.
- 1.2.2. Free factor supports of lines, rays, and subgroup systems.
- Remark.
- 1.3. Attracting laminations
- Remarks.
- 1.4. Principal automorphisms and rotationless outer automorphisms
- Remark.
- 1.5. Relative train track maps and \ct s
- 1.5.1. Definitions of relative train track maps and \cts
- Topological representatives and Nielsen paths.
- Filtrations and height.
- Directions and turns.
- Enveloping of zero strata.
- 1.5.2. Facts about \cts, their Nielsen paths, and their zero strata.
- Remark.
- Zero strata.
- 1.5.3. Facts about principal lifts, principal directions, and principal rays.
- Uniqueness of principal rays.
- Weak accumulation of attracting fixed points.
- 1.5.4. Properties of \eg strata.
- 1.6. Properties of Attracting Laminations
- 1.6.1. The relation between \eg strata and attracting laminations.
- 1.6.2. Tiles and their applications.
- Characterizing attracting laminations.
- Weak attraction of paths and circuits.
- Principal rays.
- Generic leaves.
- Construction of an attracting neighborhood basis.
- 1.6.3. \eg principal rays and \Fix_{ }
- 1.6.4. Pushing forward attracting laminations.
- Chapter 2. Geometric \eg strata and geometric laminations
- 2.1. Defining and characterizing geometric strata
- 2.1.1. Defining weak geometric models and geometric strata.
- Remark: Comparing Definition 2.2 to Definition 5.1.4 of \BookOne.
- 2.1.2. Defining geometric models.
- 2.1.3. Invariant free factor systems associated to a geometric model.
- 2.1.4. Characterizing geometric strata: Proof of Fact 2.3
- Remark.
- Remark.
- 2.2. Complementary subgraph and peripheral splitting
- 2.3. The laminations of a geometric stratum
- 2.3.1. Review of Nielsen-Thurston theory.
- Remarks on the proof.
- 2.3.2. Comparing free group laminations and surface laminations.