A universal construction for groups acting freely on real trees:
The theory of R-trees is a well-established and important area of geometric group theory and in this book the authors introduce a construction that provides a new perspective on group actions on R-trees. They construct a group RF(G), equipped with an action on an R-tree, whose elements are certain f...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2012
|
| Series: | Cambridge tracts in mathematics
195 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | The theory of R-trees is a well-established and important area of geometric group theory and in this book the authors introduce a construction that provides a new perspective on group actions on R-trees. They construct a group RF(G), equipped with an action on an R-tree, whose elements are certain functions from a compact real interval to the group G. They also study the structure of RF(G), including a detailed description of centralizers of elements and an investigation of its subgroups and quotients. Any group acting freely on an R-tree embeds in RF(G) for some choice of G. Much remains to be done to understand RF(G), and the extensive list of open problems included in an appendix could potentially lead to new methods for investigating group actions on R-trees, particularly free actions. This book will interest all geometric group theorists and model theorists whose research involves R-trees |
| Physical Description: | 1 Online-Ressource (xiii, 285 Seiten) |
| ISBN: | 9781139176064 |
| DOI: | 10.1017/CBO9781139176064 |
Staff View
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| 505 | 8 | |a 1. Introduction -- 2. The group R F (G) -- 3. The R-tree X[g subscript] associated with RF (G) -- 4. Free R-tree actions and universality -- 5. Exponent sums -- 6. Functionality -- 7. Conjugacy of hyperbolic elements -- 8. The centalisers of hyperbolic elements -- 9. Test functions: basic theory and first applications -- 10. Test functions: existence theorem and further applications -- 11. A generation to groupoids -- Appendices | |
| 520 | |a The theory of R-trees is a well-established and important area of geometric group theory and in this book the authors introduce a construction that provides a new perspective on group actions on R-trees. They construct a group RF(G), equipped with an action on an R-tree, whose elements are certain functions from a compact real interval to the group G. They also study the structure of RF(G), including a detailed description of centralizers of elements and an investigation of its subgroups and quotients. Any group acting freely on an R-tree embeds in RF(G) for some choice of G. Much remains to be done to understand RF(G), and the extensive list of open problems included in an appendix could potentially lead to new methods for investigating group actions on R-trees, particularly free actions. This book will interest all geometric group theorists and model theorists whose research involves R-trees | ||
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| 650 | 4 | |a Trees (Graph theory) | |
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| author | Chiswell, Ian 1948- |
| author_GND | (DE-588)137654995 |
| author_facet | Chiswell, Ian 1948- |
| author_role | aut |
| author_sort | Chiswell, Ian 1948- |
| author_variant | i c ic |
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| bvnumber | BV043942097 |
| classification_rvk | SK 260 |
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| contents | 1. Introduction -- 2. The group R F (G) -- 3. The R-tree X[g subscript] associated with RF (G) -- 4. Free R-tree actions and universality -- 5. Exponent sums -- 6. Functionality -- 7. Conjugacy of hyperbolic elements -- 8. The centalisers of hyperbolic elements -- 9. Test functions: basic theory and first applications -- 10. Test functions: existence theorem and further applications -- 11. A generation to groupoids -- Appendices |
| ctrlnum | (ZDB-20-CBO)CR9781139176064 (OCoLC)847033248 (DE-599)BVBBV043942097 |
| dewey-full | 512.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 |
| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139176064 |
| format | Electronic eBook |
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| id | DE-604.BV043942097 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9781139176064 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351067 |
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| physical | 1 Online-Ressource (xiii, 285 Seiten) |
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| publishDate | 2012 |
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| spelling | Chiswell, Ian 1948- Verfasser (DE-588)137654995 aut A universal construction for groups acting freely on real trees Ian Chiswell and Thomas Müller Cambridge Cambridge University Press 2012 1 Online-Ressource (xiii, 285 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 195 1. Introduction -- 2. The group R F (G) -- 3. The R-tree X[g subscript] associated with RF (G) -- 4. Free R-tree actions and universality -- 5. Exponent sums -- 6. Functionality -- 7. Conjugacy of hyperbolic elements -- 8. The centalisers of hyperbolic elements -- 9. Test functions: basic theory and first applications -- 10. Test functions: existence theorem and further applications -- 11. A generation to groupoids -- Appendices The theory of R-trees is a well-established and important area of geometric group theory and in this book the authors introduce a construction that provides a new perspective on group actions on R-trees. They construct a group RF(G), equipped with an action on an R-tree, whose elements are certain functions from a compact real interval to the group G. They also study the structure of RF(G), including a detailed description of centralizers of elements and an investigation of its subgroups and quotients. Any group acting freely on an R-tree embeds in RF(G) for some choice of G. Much remains to be done to understand RF(G), and the extensive list of open problems included in an appendix could potentially lead to new methods for investigating group actions on R-trees, particularly free actions. This book will interest all geometric group theorists and model theorists whose research involves R-trees Geometric group theory Trees (Graph theory) Müller, Thomas 1957- Sonstige oth Erscheint auch als Druck-Ausgabe 978-1-107-02481-6 https://doi.org/10.1017/CBO9781139176064 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Chiswell, Ian 1948- A universal construction for groups acting freely on real trees 1. Introduction -- 2. The group R F (G) -- 3. The R-tree X[g subscript] associated with RF (G) -- 4. Free R-tree actions and universality -- 5. Exponent sums -- 6. Functionality -- 7. Conjugacy of hyperbolic elements -- 8. The centalisers of hyperbolic elements -- 9. Test functions: basic theory and first applications -- 10. Test functions: existence theorem and further applications -- 11. A generation to groupoids -- Appendices Geometric group theory Trees (Graph theory) |
| title | A universal construction for groups acting freely on real trees |
| title_auth | A universal construction for groups acting freely on real trees |
| title_exact_search | A universal construction for groups acting freely on real trees |
| title_full | A universal construction for groups acting freely on real trees Ian Chiswell and Thomas Müller |
| title_fullStr | A universal construction for groups acting freely on real trees Ian Chiswell and Thomas Müller |
| title_full_unstemmed | A universal construction for groups acting freely on real trees Ian Chiswell and Thomas Müller |
| title_short | A universal construction for groups acting freely on real trees |
| title_sort | a universal construction for groups acting freely on real trees |
| topic | Geometric group theory Trees (Graph theory) |
| topic_facet | Geometric group theory Trees (Graph theory) |
| url | https://doi.org/10.1017/CBO9781139176064 |
| work_keys_str_mv | AT chiswellian auniversalconstructionforgroupsactingfreelyonrealtrees AT mullerthomas auniversalconstructionforgroupsactingfreelyonrealtrees |