Author: Klaus Johannson
Publisher: Springer
ISBN: 3540491813
Category : Mathematics
Languages : en
Pages : 464
Book Description
This book is a study of combinatorial structures of 3-mani- folds, especially Haken 3-manifolds. Specifically, it is concerned with Heegard graphs in Haken 3-manifolds, i.e., with graphs whose complements have a free fundamental group. These graphs always exist. They fix not only a combinatorial stucture but also a presentation for the fundamental group of the underlying 3-manifold. The starting point of the book is the result that the intersection of Heegard graphs with incompressible surfaces, or hierarchies of such surfaces, is very rigid. A number of finiteness results lead up to a ri- gidity theorem for Heegard graphs. The book is intended for graduate students and researchers in low-dimensional topolo- gy as well as combinatorial theory. It is self-contained and requires only a basic knowledge of the theory of 3-manifolds
Topology and Combinatorics of 3-Manifolds
Author: Klaus Johannson
Publisher: Springer
ISBN: 3540491813
Category : Mathematics
Languages : en
Pages : 464
Book Description
This book is a study of combinatorial structures of 3-mani- folds, especially Haken 3-manifolds. Specifically, it is concerned with Heegard graphs in Haken 3-manifolds, i.e., with graphs whose complements have a free fundamental group. These graphs always exist. They fix not only a combinatorial stucture but also a presentation for the fundamental group of the underlying 3-manifold. The starting point of the book is the result that the intersection of Heegard graphs with incompressible surfaces, or hierarchies of such surfaces, is very rigid. A number of finiteness results lead up to a ri- gidity theorem for Heegard graphs. The book is intended for graduate students and researchers in low-dimensional topolo- gy as well as combinatorial theory. It is self-contained and requires only a basic knowledge of the theory of 3-manifolds
Publisher: Springer
ISBN: 3540491813
Category : Mathematics
Languages : en
Pages : 464
Book Description
This book is a study of combinatorial structures of 3-mani- folds, especially Haken 3-manifolds. Specifically, it is concerned with Heegard graphs in Haken 3-manifolds, i.e., with graphs whose complements have a free fundamental group. These graphs always exist. They fix not only a combinatorial stucture but also a presentation for the fundamental group of the underlying 3-manifold. The starting point of the book is the result that the intersection of Heegard graphs with incompressible surfaces, or hierarchies of such surfaces, is very rigid. A number of finiteness results lead up to a ri- gidity theorem for Heegard graphs. The book is intended for graduate students and researchers in low-dimensional topolo- gy as well as combinatorial theory. It is self-contained and requires only a basic knowledge of the theory of 3-manifolds
The Geometric Topology of 3-manifolds
Author: R. H. Bing
Publisher: American Mathematical Soc.
ISBN: 0821810405
Category : Mathematics
Languages : en
Pages : 250
Book Description
Suitable for students and researchers in topology. this work provides the reader with an understanding of the physical properties of Euclidean 3-space - the space in which we presume we live.
Publisher: American Mathematical Soc.
ISBN: 0821810405
Category : Mathematics
Languages : en
Pages : 250
Book Description
Suitable for students and researchers in topology. this work provides the reader with an understanding of the physical properties of Euclidean 3-space - the space in which we presume we live.
Algorithmic Topology and Classification of 3-Manifolds
Author: Sergei Matveev
Publisher: Springer Science & Business Media
ISBN: 9783540441717
Category : Mathematics
Languages : en
Pages : 504
Book Description
Here is a thorough review of topics in 3-dimensional topology, derived from a decade of courses taught by the author. The author keeps the exposition to an elementary level by presenting the material mainly from the point of view of special polyhedra and special spines of 3-manifolds. The book culminates with the recognition procedure for Haken manifolds, and includes up-to-date results in computer enumeration of 3-mainfolds. The second edition adds new results, new proofs, and commentaries. Algorithmic Topology and Classification of 3-Manifolds serves as a standard reference for algorithmic 3-dimensional topology for both graduate students and researchers.
Publisher: Springer Science & Business Media
ISBN: 9783540441717
Category : Mathematics
Languages : en
Pages : 504
Book Description
Here is a thorough review of topics in 3-dimensional topology, derived from a decade of courses taught by the author. The author keeps the exposition to an elementary level by presenting the material mainly from the point of view of special polyhedra and special spines of 3-manifolds. The book culminates with the recognition procedure for Haken manifolds, and includes up-to-date results in computer enumeration of 3-mainfolds. The second edition adds new results, new proofs, and commentaries. Algorithmic Topology and Classification of 3-Manifolds serves as a standard reference for algorithmic 3-dimensional topology for both graduate students and researchers.
Lectures on the Topology of 3-Manifolds
Author: Nikolai Saveliev
Publisher: Walter de Gruyter
ISBN: 3110806355
Category : Mathematics
Languages : en
Pages : 212
Book Description
Publisher: Walter de Gruyter
ISBN: 3110806355
Category : Mathematics
Languages : en
Pages : 212
Book Description
3-manifolds
Author: John Hempel
Publisher: American Mathematical Soc.
ISBN:
Category : Manifolds (Mathematics)
Languages : en
Pages : 220
Book Description
Publisher: American Mathematical Soc.
ISBN:
Category : Manifolds (Mathematics)
Languages : en
Pages : 220
Book Description
Representing 3-manifolds By Filling Dehn Surfaces
Author: Ruben Vigara Benito
Publisher: World Scientific
ISBN: 9814725501
Category : Mathematics
Languages : en
Pages : 299
Book Description
This book provides an introduction to the beautiful and deep subject of filling Dehn surfaces in the study of topological 3-manifolds. This book presents, for the first time in English and with all the details, the results from the PhD thesis of the first author, together with some more recent results in the subject. It also presents some key ideas on how these techniques could be used on other subjects.Representing 3-Manifolds by Filling Dehn Surfaces is mostly self-contained requiring only basic knowledge on topology and homotopy theory. The complete and detailed proofs are illustrated with a set of more than 600 spectacular pictures, in the tradition of low-dimensional topology books. It is a basic reference for researchers in the area, but it can also be used as an advanced textbook for graduate students or even for adventurous undergraduates in mathematics. The book uses topological and combinatorial tools developed throughout the twentieth century making the volume a trip along the history of low-dimensional topology.
Publisher: World Scientific
ISBN: 9814725501
Category : Mathematics
Languages : en
Pages : 299
Book Description
This book provides an introduction to the beautiful and deep subject of filling Dehn surfaces in the study of topological 3-manifolds. This book presents, for the first time in English and with all the details, the results from the PhD thesis of the first author, together with some more recent results in the subject. It also presents some key ideas on how these techniques could be used on other subjects.Representing 3-Manifolds by Filling Dehn Surfaces is mostly self-contained requiring only basic knowledge on topology and homotopy theory. The complete and detailed proofs are illustrated with a set of more than 600 spectacular pictures, in the tradition of low-dimensional topology books. It is a basic reference for researchers in the area, but it can also be used as an advanced textbook for graduate students or even for adventurous undergraduates in mathematics. The book uses topological and combinatorial tools developed throughout the twentieth century making the volume a trip along the history of low-dimensional topology.
Introduction to 3-Manifolds
Author: Jennifer Schultens
Publisher: American Mathematical Soc.
ISBN: 1470410206
Category : Mathematics
Languages : en
Pages : 298
Book Description
This book grew out of a graduate course on 3-manifolds and is intended for a mathematically experienced audience that is new to low-dimensional topology. The exposition begins with the definition of a manifold, explores possible additional structures on manifolds, discusses the classification of surfaces, introduces key foundational results for 3-manifolds, and provides an overview of knot theory. It then continues with more specialized topics by briefly considering triangulations of 3-manifolds, normal surface theory, and Heegaard splittings. The book finishes with a discussion of topics relevant to viewing 3-manifolds via the curve complex. With about 250 figures and more than 200 exercises, this book can serve as an excellent overview and starting point for the study of 3-manifolds.
Publisher: American Mathematical Soc.
ISBN: 1470410206
Category : Mathematics
Languages : en
Pages : 298
Book Description
This book grew out of a graduate course on 3-manifolds and is intended for a mathematically experienced audience that is new to low-dimensional topology. The exposition begins with the definition of a manifold, explores possible additional structures on manifolds, discusses the classification of surfaces, introduces key foundational results for 3-manifolds, and provides an overview of knot theory. It then continues with more specialized topics by briefly considering triangulations of 3-manifolds, normal surface theory, and Heegaard splittings. The book finishes with a discussion of topics relevant to viewing 3-manifolds via the curve complex. With about 250 figures and more than 200 exercises, this book can serve as an excellent overview and starting point for the study of 3-manifolds.
Renormalization and 3-manifolds which Fiber Over the Circle
Author: Curtis T. McMullen
Publisher: Princeton University Press
ISBN: 0691011532
Category : Mathematics
Languages : en
Pages : 263
Book Description
Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitative proof of convergence of renormalization.
Publisher: Princeton University Press
ISBN: 0691011532
Category : Mathematics
Languages : en
Pages : 263
Book Description
Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitative proof of convergence of renormalization.
Lectures on Three-Manifold Topology
Author: William H. Jaco
Publisher: American Mathematical Soc.
ISBN: 0821816934
Category : Mathematics
Languages : en
Pages : 266
Book Description
This manuscript is a detailed presentation of the ten lectures given by the author at the NSF Regional Conference on Three-Manifold Topology, held October 1977, at Virginia Polytechnic Institute and State University. The purpose of the conference was to present the current state of affairs in three-manifold topology and to integrate the classical results with the many recent advances and new directions.
Publisher: American Mathematical Soc.
ISBN: 0821816934
Category : Mathematics
Languages : en
Pages : 266
Book Description
This manuscript is a detailed presentation of the ten lectures given by the author at the NSF Regional Conference on Three-Manifold Topology, held October 1977, at Virginia Polytechnic Institute and State University. The purpose of the conference was to present the current state of affairs in three-manifold topology and to integrate the classical results with the many recent advances and new directions.
Topology of 3-manifolds
Author: Marion Kirkland Fort
Publisher:
ISBN:
Category : Algebraic topology
Languages : en
Pages : 280
Book Description
Publisher:
ISBN:
Category : Algebraic topology
Languages : en
Pages : 280
Book Description