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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 |
MARC
| LEADER | 00000cam a2200000Mu 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_on1206396989 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
| 007 | cr ||||||||||| | ||
| 008 | 201114s2020 riu o ||| 0 eng d | ||
| 040 | |a EBLCP |b eng |c EBLCP |d LOA |d OCLCO |d OCLCF |d OCLCO |d OCLCQ |d OCLCO |d OCLCL | ||
| 020 | |a 9781470458027 | ||
| 020 | |a 1470458020 | ||
| 029 | 1 | |a AU@ |b 000069468713 | |
| 035 | |a (OCoLC)1206396989 | ||
| 050 | 4 | |a QA174.2 |b .H363 2020 | |
| 082 | 0 | 4 | |a 511.3/26 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Handel, Michael. | |
| 245 | 1 | 0 | |a Subgroup Decomposition in Mathrm{Out}(F_{n}) |h [electronic resource]. |
| 260 | |a Providence : |b American Mathematical Society, |c 2020. | ||
| 300 | |a 1 online resource (290 p.). | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society Ser. ; |v v.264 | |
| 500 | |a Description based upon print version of record. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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. | |
| 500 | |a 2.3.3. Application: The inclusion lattice of attracting laminations. | ||
| 520 | |a 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. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Non-Abelian groups. | |
| 650 | 0 | |a Geometric group theory. | |
| 650 | 0 | |a Decomposition (Mathematics) | |
| 650 | 0 | |a Automorphisms. | |
| 650 | 0 | |a Algebraic topology. | |
| 650 | 6 | |a Groupes non abéliens. | |
| 650 | 6 | |a Théorie géométrique des groupes. | |
| 650 | 6 | |a Décomposition (Mathématiques) | |
| 650 | 6 | |a Automorphismes. | |
| 650 | 6 | |a Topologie algébrique. | |
| 650 | 7 | |a Algebraic topology |2 fast | |
| 650 | 7 | |a Automorphisms |2 fast | |
| 650 | 7 | |a Decomposition (Mathematics) |2 fast | |
| 650 | 7 | |a Geometric group theory |2 fast | |
| 650 | 7 | |a Non-Abelian groups |2 fast | |
| 650 | 7 | |a Manifolds and cell complexes {For complex manifolds, see 32Qxx} -- Low-dimensional topology -- Topological methods in group theory. |2 msc | |
| 650 | 7 | |a Group theory and generalizations -- Structure and classification of infinite or finite groups -- Free nonabelian groups. |2 msc | |
| 650 | 7 | |a Group theory and generalizations -- Special aspects of infinite or finite groups -- Geometric group theory [See also 05C25, 20E08, 57Mxx]. |2 msc | |
| 650 | 7 | |a Group theory and generalizations -- Special aspects of infinite or finite groups -- Automorphism groups of groups [See also 20E36]. |2 msc | |
| 700 | 1 | |a Mosher, Lee. | |
| 758 | |i has work: |a Subgroup Decomposition in Mathrm{Out}(F_{n}) (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGRTQbvbjgqpBhYfg4TM8C |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Handel, Michael |t Subgroup Decomposition in Mathrm{Out}(F_{n}) |d Providence : American Mathematical Society,c2020 |z 9781470441135 |
| 830 | 0 | |a Memoirs of the American Mathematical Society Ser. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=6195959 |z Texto completo |
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL6195959 | ||
| 994 | |a 92 |b IZTAP | ||