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Combinatorics of Train Tracks by R.C. Penner (English) Hardcover SEALED NEW
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eBay item number:205869472380
Item specifics
- Condition
- Brand New: A new, unread, unused book in perfect condition with no missing or damaged pages. See all condition definitionsopens in a new window or tab
- Book Title
- Combinatorics of Train Tracks
- ISBN-13
- 9780691025315
- ISBN
- 9780691025315
About this product
Product Identifiers
Publisher
Princeton University Press
ISBN-10
0691025312
ISBN-13
9780691025315
eBay Product ID (ePID)
524404
Product Key Features
Number of Pages
232 Pages
Publication Name
Combinatorics of Train Tracks
Language
English
Publication Year
1991
Subject
Topology, Combinatorics
Type
Textbook
Subject Area
Mathematics
Series
Annals of Mathematics Studies
Format
Trade Paperback
Dimensions
Item Height
0.6 in
Item Weight
12.7 Oz
Item Length
9.2 in
Item Width
6.1 in
Additional Product Features
Intended Audience
College Audience
Reviews
The book is beautifully written, with a clear path of theoretical development amid a wealth of detail for the technician. . . . [T]his text provides a valuable reference work as well as a readable introduction for the student or newcomer to the area. -- Zentralblatt for Mathematik, "The book is beautifully written, with a clear path of theoretical development amid a wealth of detail for the technician. . . . [T]his text provides a valuable reference work as well as a readable introduction for the student or newcomer to the area."-- Zentralblatt f'r Mathematik, "The book is beautifully written, with a clear path of theoretical development amid a wealth of detail for the technician. . . . [T]his text provides a valuable reference work as well as a readable introduction for the student or newcomer to the area."-- Zentralblatt fr Mathematik, The book is beautifully written, with a clear path of theoretical development amid a wealth of detail for the technician. . . . [T]his text provides a valuable reference work as well as a readable introduction for the student or newcomer to the area., "The book is beautifully written, with a clear path of theoretical development amid a wealth of detail for the technician. . . . [T]his text provides a valuable reference work as well as a readable introduction for the student or newcomer to the area." -- Zentralblatt fòr Mathematik, The book is beautifully written, with a clear path of theoretical development amid a wealth of detail for the technician. . . . [T]his text provides a valuable reference work as well as a readable introduction for the student or newcomer to the area. -- Zentralblatt fr Mathematik, The book is beautifully written, with a clear path of theoretical development amid a wealth of detail for the technician. . . . [T]his text provides a valuable reference work as well as a readable introduction for the student or newcomer to the area. -- Zentralblatt fòr Mathematik, "The book is beautifully written, with a clear path of theoretical development amid a wealth of detail for the technician. . . . [T]his text provides a valuable reference work as well as a readable introduction for the student or newcomer to the area." -- Zentralblatt fr Mathematik, "The book is beautifully written, with a clear path of theoretical development amid a wealth of detail for the technician. . . . [T]his text provides a valuable reference work as well as a readable introduction for the student or newcomer to the area."-- Zentralblatt fòr Mathematik
Series Volume Number
125
Table Of Content
Preface Acknowledgements Ch. 1 The Basic Theory 3 1.1 Train Tracks 4 1.2 Multiple Curves and Dehn's Theorem 10 1.3 Recurrence and Transverse Recurrence 18 1.4 Genericity and Transverse Recurrence 39 1.5 Trainpaths and Transverse Recurrence 60 1.6 Laminations 68 1.7 Measured Laminations 82 1.8 Bounded Surfaces and Tracks with Stops 102 Ch. 2 Combinatorial Equivalence 115 2.1 Splitting, Shifting, and Carrying 116 2.2 Equivalence of Birecurrent Train Tracks 124 2.3 Splitting versus Shifting 127 2.4 Equivalence versus Carrying 133 2.5 Splitting and Efficiency 139 2.6 The Standard Models 145 2.7 Existence of the Standard Models 154 2.8 Uniqueness of the Standard Models 160 Ch. 3 The Structure of ML[subscript 0] 173 3.1 The Topology of ML[subscript 0] and PL[subscript 0] 174 3.2 The Symplectic Structure of ML[subscript 0] 182 3.3 Topological Equivalence 188 3.4 Duality and Tangential Coordinates 191 Epilogue 204 Addendum The Action of Mapping Classes on ML[subscript 0] 210 Bibliography 214
Synopsis
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 treatment of the combinatorial structure of the space of measured geodesic laminations in a fixed 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., 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 treatment of the 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.
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- k***l (249)- Feedback left by buyer.Past monthVerified purchaseA great book by a trusted expositor. A great seller! The book was in a much better condition than described, very well packaged and shipped quickly! Thanks so much and God bless!
- n***s (301)- Feedback left by buyer.Past 6 monthsVerified purchaseItem exactly as described, packaged good and arrived quickly - this was my first tackle-box my parents purchased for me from our local Kmart Store - "smile"
- 6***l (211)- Feedback left by buyer.Past monthVerified purchaseBook as described. Packaged securely, and shipped promptly. Thank you, highly recommend. A+++
Popular categories from this store
Seller feedback (1,025)
- k***l (249)- Feedback left by buyer.Past monthVerified purchaseA great book by a trusted expositor. A great seller! The book was in a much better condition than described, very well packaged and shipped quickly! Thanks so much and God bless!
- n***s (301)- Feedback left by buyer.Past 6 monthsVerified purchaseItem exactly as described, packaged good and arrived quickly - this was my first tackle-box my parents purchased for me from our local Kmart Store - "smile"
- 6***l (211)- Feedback left by buyer.Past monthVerified purchaseBook as described. Packaged securely, and shipped promptly. Thank you, highly recommend. A+++