Combinatorics Of Train Tracks Am 125 Volume 125
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Combinatorics Of Train Tracks Am 125 Volume 125
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Author : R. C. Penner
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Combinatorics Of Train Tracks Am 125 Volume 125 written by R. C. Penner and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
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.
Combinatorics Of Train Tracks
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Author : R. C. Penner
language : en
Publisher:
Release Date : 1992
Combinatorics Of Train Tracks written by R. C. Penner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
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.
Geometry Topology And Dynamics Of Character Varieties
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Author : William Goldman
language : en
Publisher: World Scientific
Release Date : 2012-06-18
Geometry Topology And Dynamics Of Character Varieties written by William Goldman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-18 with Mathematics categories.
This volume is based on lectures given at the highly successful three-week Summer School on Geometry, Topology and Dynamics of Character Varieties held at the National University of Singapore's Institute for Mathematical Sciences in July 2010.Aimed at graduate students in the early stages of research, the edited and refereed articles comprise an excellent introduction to the subject of the program, much of which is otherwise available only in specialized texts. Topics include hyperbolic structures on surfaces and their degenerations, applications of ping-pong lemmas in various contexts, introductions to Lorenzian and complex hyperbolic geometry, and representation varieties of surface groups into PSL(2, ℝ) and other semi-simple Lie groups. This volume will serve as a useful portal to students and researchers in a vibrant and multi-faceted area of mathematics.
Braids And Dynamics
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Author : Jean-Luc Thiffeault
language : en
Publisher: Springer Nature
Release Date : 2022-09-05
Braids And Dynamics written by Jean-Luc Thiffeault and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-05 with Mathematics categories.
This monograph uses braids to explore dynamics on surfaces, with an eye towards applications to mixing in fluids. The text uses the particular example of taffy pulling devices to represent pseudo-Anosov maps in practice. In addition, its final chapters also briefly discuss current applications in the emerging field of analyzing braids created from trajectory data. While written with beginning graduate students, advanced undergraduates, or practicing applied mathematicians in mind, the book is also suitable for pure mathematicians seeking real-world examples. Readers can benefit from some knowledge of homotopy and homology groups, but these concepts are briefly reviewed. Some familiarity with Matlab is also helpful for the computational examples.
Surveys On Surgery Theory Papers Dedicated To C T C Wall
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Author : Sylvain Cappell
language : en
Publisher: Princeton University Press
Release Date : 2000
Surveys On Surgery Theory Papers Dedicated To C T C Wall written by Sylvain Cappell and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
Bulletin New Series Of The American Mathematical Society
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Author :
language : en
Publisher:
Release Date : 1993
Bulletin New Series Of The American Mathematical Society written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
Bulletin Of The American Mathematical Society
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Author :
language : en
Publisher:
Release Date : 1993
Bulletin Of The American Mathematical Society written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
Invariants Of Knots And 3 Manifolds Kyoto 2001
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Author : Tomotada Ohtsuki
language : en
Publisher:
Release Date : 2002
Invariants Of Knots And 3 Manifolds Kyoto 2001 written by Tomotada Ohtsuki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Knot theory categories.
Subject Guide To Children S Books In Print 1997
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Author : Bowker Editorial Staff
language : en
Publisher: R. R. Bowker
Release Date : 1996-09
Subject Guide To Children S Books In Print 1997 written by Bowker Editorial Staff and has been published by R. R. Bowker this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-09 with Reference categories.
Subject Guide To Books In Print
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Author :
language : en
Publisher:
Release Date : 1975
Subject Guide To Books In Print written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with American literature categories.