Introduction to [lambda]-trees /:
"The theory of [lambda]-trees has its origin in the work of Lyndon on length functions in groups. The first definition of an R-tree was given by Tits in 1977. The importance of [lambda]-trees was established by Morgan and Shalen, who showed how to compactify a generalisation of Teichmüller spa...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; River Edge, N.J. :
World Scientific,
©2001.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "The theory of [lambda]-trees has its origin in the work of Lyndon on length functions in groups. The first definition of an R-tree was given by Tits in 1977. The importance of [lambda]-trees was established by Morgan and Shalen, who showed how to compactify a generalisation of Teichmüller space for a finitely generated group using R-trees. In that work they were led to define the idea of a [lambda]-tree, where [lambda] is an arbitrary ordered abelian group. Since then there has been much progress in understanding the structure of groups acting on R-trees, notably Rips' theorem on free actions. There has also been some progress for certain other ordered abelian groups [lambda], including some interesting connections with model theory. Introduction to [lambda]-Trees will prove to be useful for mathematicians and research students in algebra and topology." |
| Beschreibung: | 1 online resource (x, 315 pages :) |
| Bibliographie: | Includes bibliographical references (pages 297-305) and index. |
| ISBN: | 9789812810533 9812810536 128195621X 9781281956217 |
Internformat
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| 245 | 1 | 0 | |a Introduction to [lambda]-trees / |c Ian Chiswell. |
| 260 | |a Singapore ; |a River Edge, N.J. : |b World Scientific, |c ©2001. | ||
| 300 | |a 1 online resource (x, 315 pages :) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 504 | |a Includes bibliographical references (pages 297-305) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Ch. 1. Preliminaries. 1. Ordered abelian groups. 2. Metric spaces. 3. Graphs and simplicial trees. 4. Valuations -- ch. 2. [lambda]-trees and their construction. 1. Definition and elementary properties. 2. Special properties of R-trees. 3. Linear subtrees and ends. 4. Lyndon length functions -- ch. 3. Isometries of [lambda]-trees. 1. Theory of a single isometry. 2. Group actions as isometries. 3. Pairs of isometries. 4. Minimal actions -- ch. 4. Aspects of group actions on [lambda]-trees. 1. Introduction. 2. Actions of special classes of groups. 3. The action of the special linear group. 4. Measured laminations. 5. Hyperbolic surfaces. 6. Spaces of actions on R-trees -- ch. 5. Free actions. 1. Introduction. 2. Harrison's theorem. 3. Some examples. 4. Free actions of surface groups. 5. Non-standard free groups -- ch. 6. Rips' theorem. 1. Systems of isometries. 2. Minimal components. 3. Independent generators. 4. Interval exchanges and conclusion. | |
| 520 | |a "The theory of [lambda]-trees has its origin in the work of Lyndon on length functions in groups. The first definition of an R-tree was given by Tits in 1977. The importance of [lambda]-trees was established by Morgan and Shalen, who showed how to compactify a generalisation of Teichmüller space for a finitely generated group using R-trees. In that work they were led to define the idea of a [lambda]-tree, where [lambda] is an arbitrary ordered abelian group. Since then there has been much progress in understanding the structure of groups acting on R-trees, notably Rips' theorem on free actions. There has also been some progress for certain other ordered abelian groups [lambda], including some interesting connections with model theory. Introduction to [lambda]-Trees will prove to be useful for mathematicians and research students in algebra and topology." | ||
| 650 | 0 | |a Lambda algebra. |0 http://id.loc.gov/authorities/subjects/sh85074173 | |
| 650 | 0 | |a Trees (Graph theory) |0 http://id.loc.gov/authorities/subjects/sh85137259 | |
| 650 | 0 | |a Group theory. |0 http://id.loc.gov/authorities/subjects/sh85057512 | |
| 650 | 6 | |a Lambda-algèbre. | |
| 650 | 6 | |a Arbres (Théorie des graphes) | |
| 650 | 6 | |a Théorie des groupes. | |
| 650 | 7 | |a MATHEMATICS |x Graphic Methods. |2 bisacsh | |
| 650 | 7 | |a Group theory |2 fast | |
| 650 | 7 | |a Lambda algebra |2 fast | |
| 650 | 7 | |a Trees (Graph theory) |2 fast | |
| 650 | 7 | |a Teoria dos grupos. |2 larpcal | |
| 650 | 7 | |a Teoria dos modelos. |2 larpcal | |
| 650 | 7 | |a Lógica matemática. |2 larpcal | |
| 650 | 7 | |a Árvores. |2 larpcal | |
| 758 | |i has work: |a Introduction to [lambda]-trees (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFvBrfxKjGYfFP79xRVxTb |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Chiswell, Ian, 1948- |t Introduction to [lambda]-trees. |d Singapore ; River Edge, N.J. : World Scientific, ©2001 |z 9810243863 |z 9789810243869 |w (DLC) 2001281032 |w (OCoLC)47032651 |
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Datensatz im Suchindex
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| _version_ | 1813903328659111937 |
| adam_text | |
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| author | Chiswell, Ian, 1948- |
| author_GND | http://id.loc.gov/authorities/names/n00014668 |
| author_facet | Chiswell, Ian, 1948- |
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| contents | Ch. 1. Preliminaries. 1. Ordered abelian groups. 2. Metric spaces. 3. Graphs and simplicial trees. 4. Valuations -- ch. 2. [lambda]-trees and their construction. 1. Definition and elementary properties. 2. Special properties of R-trees. 3. Linear subtrees and ends. 4. Lyndon length functions -- ch. 3. Isometries of [lambda]-trees. 1. Theory of a single isometry. 2. Group actions as isometries. 3. Pairs of isometries. 4. Minimal actions -- ch. 4. Aspects of group actions on [lambda]-trees. 1. Introduction. 2. Actions of special classes of groups. 3. The action of the special linear group. 4. Measured laminations. 5. Hyperbolic surfaces. 6. Spaces of actions on R-trees -- ch. 5. Free actions. 1. Introduction. 2. Harrison's theorem. 3. Some examples. 4. Free actions of surface groups. 5. Non-standard free groups -- ch. 6. Rips' theorem. 1. Systems of isometries. 2. Minimal components. 3. Independent generators. 4. Interval exchanges and conclusion. |
| ctrlnum | (OCoLC)268962256 |
| dewey-full | 511/.52 |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.52 |
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| discipline | Mathematik |
| format | Electronic eBook |
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| indexdate | 2024-10-25T16:16:56Z |
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| publisher | World Scientific, |
| record_format | marc |
| spelling | Chiswell, Ian, 1948- https://id.oclc.org/worldcat/entity/E39PCjrQdvHQbCMVPGymgx4JcP http://id.loc.gov/authorities/names/n00014668 Introduction to [lambda]-trees / Ian Chiswell. Singapore ; River Edge, N.J. : World Scientific, ©2001. 1 online resource (x, 315 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 297-305) and index. Print version record. Ch. 1. Preliminaries. 1. Ordered abelian groups. 2. Metric spaces. 3. Graphs and simplicial trees. 4. Valuations -- ch. 2. [lambda]-trees and their construction. 1. Definition and elementary properties. 2. Special properties of R-trees. 3. Linear subtrees and ends. 4. Lyndon length functions -- ch. 3. Isometries of [lambda]-trees. 1. Theory of a single isometry. 2. Group actions as isometries. 3. Pairs of isometries. 4. Minimal actions -- ch. 4. Aspects of group actions on [lambda]-trees. 1. Introduction. 2. Actions of special classes of groups. 3. The action of the special linear group. 4. Measured laminations. 5. Hyperbolic surfaces. 6. Spaces of actions on R-trees -- ch. 5. Free actions. 1. Introduction. 2. Harrison's theorem. 3. Some examples. 4. Free actions of surface groups. 5. Non-standard free groups -- ch. 6. Rips' theorem. 1. Systems of isometries. 2. Minimal components. 3. Independent generators. 4. Interval exchanges and conclusion. "The theory of [lambda]-trees has its origin in the work of Lyndon on length functions in groups. The first definition of an R-tree was given by Tits in 1977. The importance of [lambda]-trees was established by Morgan and Shalen, who showed how to compactify a generalisation of Teichmüller space for a finitely generated group using R-trees. In that work they were led to define the idea of a [lambda]-tree, where [lambda] is an arbitrary ordered abelian group. Since then there has been much progress in understanding the structure of groups acting on R-trees, notably Rips' theorem on free actions. There has also been some progress for certain other ordered abelian groups [lambda], including some interesting connections with model theory. Introduction to [lambda]-Trees will prove to be useful for mathematicians and research students in algebra and topology." Lambda algebra. http://id.loc.gov/authorities/subjects/sh85074173 Trees (Graph theory) http://id.loc.gov/authorities/subjects/sh85137259 Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Lambda-algèbre. Arbres (Théorie des graphes) Théorie des groupes. MATHEMATICS Graphic Methods. bisacsh Group theory fast Lambda algebra fast Trees (Graph theory) fast Teoria dos grupos. larpcal Teoria dos modelos. larpcal Lógica matemática. larpcal Árvores. larpcal has work: Introduction to [lambda]-trees (Text) https://id.oclc.org/worldcat/entity/E39PCFvBrfxKjGYfFP79xRVxTb https://id.oclc.org/worldcat/ontology/hasWork Print version: Chiswell, Ian, 1948- Introduction to [lambda]-trees. Singapore ; River Edge, N.J. : World Scientific, ©2001 9810243863 9789810243869 (DLC) 2001281032 (OCoLC)47032651 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235901 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235901 Volltext |
| spellingShingle | Chiswell, Ian, 1948- Introduction to [lambda]-trees / Ch. 1. Preliminaries. 1. Ordered abelian groups. 2. Metric spaces. 3. Graphs and simplicial trees. 4. Valuations -- ch. 2. [lambda]-trees and their construction. 1. Definition and elementary properties. 2. Special properties of R-trees. 3. Linear subtrees and ends. 4. Lyndon length functions -- ch. 3. Isometries of [lambda]-trees. 1. Theory of a single isometry. 2. Group actions as isometries. 3. Pairs of isometries. 4. Minimal actions -- ch. 4. Aspects of group actions on [lambda]-trees. 1. Introduction. 2. Actions of special classes of groups. 3. The action of the special linear group. 4. Measured laminations. 5. Hyperbolic surfaces. 6. Spaces of actions on R-trees -- ch. 5. Free actions. 1. Introduction. 2. Harrison's theorem. 3. Some examples. 4. Free actions of surface groups. 5. Non-standard free groups -- ch. 6. Rips' theorem. 1. Systems of isometries. 2. Minimal components. 3. Independent generators. 4. Interval exchanges and conclusion. Lambda algebra. http://id.loc.gov/authorities/subjects/sh85074173 Trees (Graph theory) http://id.loc.gov/authorities/subjects/sh85137259 Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Lambda-algèbre. Arbres (Théorie des graphes) Théorie des groupes. MATHEMATICS Graphic Methods. bisacsh Group theory fast Lambda algebra fast Trees (Graph theory) fast Teoria dos grupos. larpcal Teoria dos modelos. larpcal Lógica matemática. larpcal Árvores. larpcal |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85074173 http://id.loc.gov/authorities/subjects/sh85137259 http://id.loc.gov/authorities/subjects/sh85057512 |
| title | Introduction to [lambda]-trees / |
| title_auth | Introduction to [lambda]-trees / |
| title_exact_search | Introduction to [lambda]-trees / |
| title_full | Introduction to [lambda]-trees / Ian Chiswell. |
| title_fullStr | Introduction to [lambda]-trees / Ian Chiswell. |
| title_full_unstemmed | Introduction to [lambda]-trees / Ian Chiswell. |
| title_short | Introduction to [lambda]-trees / |
| title_sort | introduction to lambda trees |
| topic | Lambda algebra. http://id.loc.gov/authorities/subjects/sh85074173 Trees (Graph theory) http://id.loc.gov/authorities/subjects/sh85137259 Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Lambda-algèbre. Arbres (Théorie des graphes) Théorie des groupes. MATHEMATICS Graphic Methods. bisacsh Group theory fast Lambda algebra fast Trees (Graph theory) fast Teoria dos grupos. larpcal Teoria dos modelos. larpcal Lógica matemática. larpcal Árvores. larpcal |
| topic_facet | Lambda algebra. Trees (Graph theory) Group theory. Lambda-algèbre. Arbres (Théorie des graphes) Théorie des groupes. MATHEMATICS Graphic Methods. Group theory Lambda algebra Teoria dos grupos. Teoria dos modelos. Lógica matemática. Árvores. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235901 |
| work_keys_str_mv | AT chiswellian introductiontolambdatrees |