Combinatorics of train tracks:
Measured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in two-and three-dimensional topology, geometry, and dynamical systems. This book presents a self-contained and comprehensive treatment of the rich co...
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[1992]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 125 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1515/9781400882458?locatt=mode:legacy |
| Zusammenfassung: | Measured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in two-and three-dimensional topology, geometry, and dynamical systems. This book presents a self-contained and comprehensive treatment of the rich combinatorial structure of the space of measured geodesic laminations in a fixed surface. Families of measured geodesic laminations are described by specifying a train track in the surface, and the space of measured geodesic laminations is analyzed by studying properties of train tracks in the surface. The material is developed from first principles, the techniques employed are essentially combinatorial, and only a minimal background is required on the part of the reader. Specifically, familiarity with elementary differential topology and hyperbolic geometry is assumed. The first chapter treats the basic theory of train tracks as discovered by W. P. Thurston, including recurrence, transverse recurrence, and the explicit construction of a measured geodesic lamination from a measured train track. The subsequent chapters develop certain material from R. C. Penner's thesis, including a natural equivalence relation on measured train tracks and standard models for the equivalence classes (which are used to analyze the topology and geometry of the space of measured geodesic laminations), a duality between transverse and tangential structures on a train track, and the explicit computation of the action of the mapping class group on the space of measured geodesic laminations in the surface |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) |
| Umfang: | 1 online resource |
| ISBN: | 9781400882458 |
| DOI: | 10.1515/9781400882458 |
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| 520 | |a Measured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in two-and three-dimensional topology, geometry, and dynamical systems. This book presents a self-contained and comprehensive treatment of the rich combinatorial structure of the space of measured geodesic laminations in a fixed surface. Families of measured geodesic laminations are described by specifying a train track in the surface, and the space of measured geodesic laminations is analyzed by studying properties of train tracks in the surface. The material is developed from first principles, the techniques employed are essentially combinatorial, and only a minimal background is required on the part of the reader. Specifically, familiarity with elementary differential topology and hyperbolic geometry is assumed. The first chapter treats the basic theory of train tracks as discovered by W. P. Thurston, including recurrence, transverse recurrence, and the explicit construction of a measured geodesic lamination from a measured train track. The subsequent chapters develop certain material from R. C. Penner's thesis, including a natural equivalence relation on measured train tracks and standard models for the equivalence classes (which are used to analyze the topology and geometry of the space of measured geodesic laminations), a duality between transverse and tangential structures on a train track, and the explicit computation of the action of the mapping class group on the space of measured geodesic laminations in the surface | ||
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Datensatz im Suchindex
| _version_ | 1818982189340033024 |
|---|---|
| any_adam_object | |
| author | Penner, Robert C. 1956- Harer, John L. 1952- |
| author_GND | (DE-588)172304474 (DE-588)14157528X |
| author_facet | Penner, Robert C. 1956- Harer, John L. 1952- |
| author_role | aut aut |
| author_sort | Penner, Robert C. 1956- |
| author_variant | r c p rc rcp j l h jl jlh |
| building | Verbundindex |
| bvnumber | BV043712505 |
| classification_rvk | SI 830 |
| collection | ZDB-23-DGG ZDB-23-PST |
| ctrlnum | (ZDB-23-DGG)9781400882458 (OCoLC)1165486637 (DE-599)BVBBV043712505 |
| dewey-full | 511/.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.6 |
| dewey-search | 511/.6 |
| dewey-sort | 3511 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400882458 |
| format | Electronic eBook |
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| id | DE-604.BV043712505 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:43:15Z |
| institution | BVB |
| isbn | 9781400882458 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029124733 |
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| physical | 1 online resource |
| psigel | ZDB-23-DGG ZDB-23-PST |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of Mathematics Studies |
| series2 | Annals of Mathematics Studies |
| spelling | Penner, Robert C. 1956- (DE-588)172304474 aut Combinatorics of train tracks John L. Harer, R. C. Penner Princeton, NJ Princeton University Press [1992] © 1992 1 online resource txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 125 Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) Measured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in two-and three-dimensional topology, geometry, and dynamical systems. This book presents a self-contained and comprehensive treatment of the rich combinatorial structure of the space of measured geodesic laminations in a fixed surface. Families of measured geodesic laminations are described by specifying a train track in the surface, and the space of measured geodesic laminations is analyzed by studying properties of train tracks in the surface. The material is developed from first principles, the techniques employed are essentially combinatorial, and only a minimal background is required on the part of the reader. Specifically, familiarity with elementary differential topology and hyperbolic geometry is assumed. The first chapter treats the basic theory of train tracks as discovered by W. P. Thurston, including recurrence, transverse recurrence, and the explicit construction of a measured geodesic lamination from a measured train track. The subsequent chapters develop certain material from R. C. Penner's thesis, including a natural equivalence relation on measured train tracks and standard models for the equivalence classes (which are used to analyze the topology and geometry of the space of measured geodesic laminations), a duality between transverse and tangential structures on a train track, and the explicit computation of the action of the mapping class group on the space of measured geodesic laminations in the surface In English Combinatorial analysis CW complexes Geodesics (Mathematics) Fläche (DE-588)4129864-0 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Geodäsie (DE-588)4020202-1 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf CW-Komplex (DE-588)4148419-8 gnd rswk-swf Fläche (DE-588)4129864-0 s CW-Komplex (DE-588)4148419-8 s Kombinatorische Analysis (DE-588)4164746-4 s 1\p DE-604 Geodäsie (DE-588)4020202-1 s Kombinatorik (DE-588)4031824-2 s 2\p DE-604 Harer, John L. 1952- (DE-588)14157528X aut Erscheint auch als Druck-Ausgabe 0-691-08764-4 Annals of Mathematics Studies number 125 (DE-604)BV040389493 125 https://doi.org/10.1515/9781400882458?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Penner, Robert C. 1956- Harer, John L. 1952- Combinatorics of train tracks Annals of Mathematics Studies Combinatorial analysis CW complexes Geodesics (Mathematics) Fläche (DE-588)4129864-0 gnd Kombinatorik (DE-588)4031824-2 gnd Geodäsie (DE-588)4020202-1 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd CW-Komplex (DE-588)4148419-8 gnd |
| subject_GND | (DE-588)4129864-0 (DE-588)4031824-2 (DE-588)4020202-1 (DE-588)4164746-4 (DE-588)4148419-8 |
| title | Combinatorics of train tracks |
| title_auth | Combinatorics of train tracks |
| title_exact_search | Combinatorics of train tracks |
| title_full | Combinatorics of train tracks John L. Harer, R. C. Penner |
| title_fullStr | Combinatorics of train tracks John L. Harer, R. C. Penner |
| title_full_unstemmed | Combinatorics of train tracks John L. Harer, R. C. Penner |
| title_short | Combinatorics of train tracks |
| title_sort | combinatorics of train tracks |
| topic | Combinatorial analysis CW complexes Geodesics (Mathematics) Fläche (DE-588)4129864-0 gnd Kombinatorik (DE-588)4031824-2 gnd Geodäsie (DE-588)4020202-1 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd CW-Komplex (DE-588)4148419-8 gnd |
| topic_facet | Combinatorial analysis CW complexes Geodesics (Mathematics) Fläche Kombinatorik Geodäsie Kombinatorische Analysis CW-Komplex |
| url | https://doi.org/10.1515/9781400882458?locatt=mode:legacy |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT pennerrobertc combinatoricsoftraintracks AT harerjohnl combinatoricsoftraintracks |