Algorithmic Topology and Classification of 3-Manifolds
From the reviews of the 1st edition: "This book provides a comprehensive and detailed account of different topics in algorithmic 3-dimensional topology, culminating with the recognition procedure for Haken manifolds and including the up-to-date results in
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Sergei Matveev
Algorithmic Topology and Classification of 3-Manifolds Second Edition
Algorithms and Computation in Mathematics • Volume 9 Editors Arjeh M. Cohen Henri Cohen David Eisenbud Michael F. Singer Bernd Sturmfels
Sergei Matveev
Algorithmic Topology and Classification of 3-Manifolds Second Edition
With 264 Figures and 36 Tables
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Author Sergei Matveev Chelyabinsk State University Kashirin Brothers Street, 129 Chelyabinsk 454021 Russia E-mail: [email protected]
Library of Congress Control Number: 2007927936 Mathematics Subject Classification (2000): 57M
ISSN 1431-1550 ISBN 978-3-540-45898-2 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting by the author and SPi using a Springer LATEX macro package Cover design: design & production GmbH, Heidelberg Printed on acid-free paper
SPIN: 11879817
46/SPi
543210
Preface to the First Edition
The book is devoted to algorithmic low-dimensional topology. This branch of mathematics has recently been undergoing an intense development. On the one hand, the exponential advancement of computer technologies has made it possible to conduct sophisticated computer experiments and to implement algorithmic solutions, which have in turn provided a motivation to search for new and better algorithms. On the other hand, low-dimensional topology has received an additional boost because of the discovery of numerous connections with theoretical physics. There is also another deep reason why algorithmic topology has received a lot of attention. It is that a search for algorithmic solutions generally proves to be a rich source of well-stated mathematical problems. Speaking out of my experience, it seems that an orientation towards “how to” rather than just “how is” serves as a probing stone for choosing among possible directions of research – much like problems in mechanics led once to the development of calculus. It seemed to me, when planning this book, that I had an opportunity to offer a coherent and reasonably complete account of the subject that nevertheless would be mainly accessible to graduate students. Almost all part
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