Mendeley出力
＜図書＞
Combinatorics of train tracks
| 責任表示 | by R.C. Penner with J.L. Harer |
|---|---|
| シリーズ | Annals of mathematics studies ; no. 125 |
| データ種別 | 図書 |
| 出版情報 | Princeton, N.J. : Princeton University Press , 1992 |
| 本文言語 | 英語 |
| 大きさ | xi, 216 p. : ill. ; 24 cm |
| 概要 | 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, a...d 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. 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. 続きを見る |
| 電子版へのリンク | https://hdl.handle.net/2324/6822663 |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
|---|---|---|---|---|---|---|---|---|---|---|
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理系図3F 数理独自 | PENN/10/1 | 1992 |
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068222192002227 |
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書誌詳細
| 別書名 | 異なりアクセスタイトル:Train tracks |
|---|---|
| 一般注記 | Bibliography: p. 214-216 |
| 著者標目 | *Penner, R. C., 1956- Harer, John L., 1952- |
| 件 名 | LCSH:Geodesics (Mathematics) LCSH:CW complexes LCSH:Combinatorial analysis |
| 分 類 | LCC:QA649 DC20:511/.6 NDC8:411.22 |
| 書誌ID | 1001403201 |
| ISBN | 0691087644 |
| NCID | BA13784654 |
| 巻冊次 | : cloth ; ISBN:0691087644 ; PRICE:$55.00 : pbk ; ISBN:0691025312 ; PRICE:$22.50 |
| 登録日 | 2009.11.02 |
| 更新日 | 2009.11.02 |