Ebook: Algorithmic and Computer Methods for Three-Manifolds

One service mathematics has rendered the human race. It has put common sense back where it belongs. It has put common sense back where it belongs, on the topmost shelf next to the dusty canister labelled discarded nonsense. Eric TBell Every picture tells a story. Advenisement for for Sloan's backache and kidney oils, 1907 The book you have in your hands as you are reading this, is a text on3-dimensional topology. It can serve as a pretty comprehensive text book on the subject. On the other hand, it frequently gets to the frontiers of current research in the topic. If pressed, I would initially classify it as a monograph, but, thanks to the over three hundred illustrations of the geometrical ideas involved, as a rather accessible one, and hence suitable for advanced classes. The style is somewhat informal; more or less like orally presented lectures, and the illustrations more than make up for all the visual aids and handwaving one has at one's command during an actual presentation.

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This monograph presents a comprehensive coverage of three-dimensional topology, as well as exploring some of its frontiers. Many important applied problems of mechanics and theoretical physics can be reduced to algorithmic problems of three-dimensional topology, which can then be solved using computers. Although much progress in this field has been made in recent years, these results have not been readily accessible to a wider audience up to now. This book is based on courses the authors have given over several years, and summarises the most outstanding achievements of modern computer topology.
Audience: This book will be of interest to graduate students and researchers whose work involves such diverse disciplines as physics, mathematics, computer programmes for spline theory and its applications, geometrical modelling, geometry, and topology. The illustrations by A.T. Fomenko, drawn especially for this work, add great value and extra appeal.

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This monograph presents a comprehensive coverage of three-dimensional topology, as well as exploring some of its frontiers. Many important applied problems of mechanics and theoretical physics can be reduced to algorithmic problems of three-dimensional topology, which can then be solved using computers. Although much progress in this field has been made in recent years, these results have not been readily accessible to a wider audience up to now. This book is based on courses the authors have given over several years, and summarises the most outstanding achievements of modern computer topology.
Audience: This book will be of interest to graduate students and researchers whose work involves such diverse disciplines as physics, mathematics, computer programmes for spline theory and its applications, geometrical modelling, geometry, and topology. The illustrations by A.T. Fomenko, drawn especially for this work, add great value and extra appeal.
Content:
Front Matter....Pages i-xii
Preliminary Information....Pages 1-31
Surfaces....Pages 33-70
The Homeotopy Group of a Surface....Pages 71-108
The Presentation of Three-Dimensional Manifolds by the Identification of Faces of Polyhedra....Pages 109-122
Heegaard Splittings and Heegaard Diagrams....Pages 123-144
Algorithmic Recognition of the Sphere....Pages 145-157
Connected Sums....Pages 159-177
Knots and Links....Pages 179-205
Surgery along Links....Pages 207-228
Seifert Manifolds....Pages 229-270
Class ? ....Pages 271-286
The Haken Method....Pages 287-297
Back Matter....Pages 299-337

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This monograph presents a comprehensive coverage of three-dimensional topology, as well as exploring some of its frontiers. Many important applied problems of mechanics and theoretical physics can be reduced to algorithmic problems of three-dimensional topology, which can then be solved using computers. Although much progress in this field has been made in recent years, these results have not been readily accessible to a wider audience up to now. This book is based on courses the authors have given over several years, and summarises the most outstanding achievements of modern computer topology.
Audience: This book will be of interest to graduate students and researchers whose work involves such diverse disciplines as physics, mathematics, computer programmes for spline theory and its applications, geometrical modelling, geometry, and topology. The illustrations by A.T. Fomenko, drawn especially for this work, add great value and extra appeal.
Content:
Front Matter....Pages i-xii
Preliminary Information....Pages 1-31
Surfaces....Pages 33-70
The Homeotopy Group of a Surface....Pages 71-108
The Presentation of Three-Dimensional Manifolds by the Identification of Faces of Polyhedra....Pages 109-122
Heegaard Splittings and Heegaard Diagrams....Pages 123-144
Algorithmic Recognition of the Sphere....Pages 145-157
Connected Sums....Pages 159-177
Knots and Links....Pages 179-205
Surgery along Links....Pages 207-228
Seifert Manifolds....Pages 229-270
Class ? ....Pages 271-286
The Haken Method....Pages 287-297
Back Matter....Pages 299-337
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