Knots And Primes
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Knots And Primes
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Author : Masanori Morishita
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-27
Knots And Primes written by Masanori Morishita and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-27 with Mathematics categories.
This is a foundation for arithmetic topology - a new branch of mathematics which is focused upon the analogy between knot theory and number theory. Starting with an informative introduction to its origins, namely Gauss, this text provides a background on knots, three manifolds and number fields. Common aspects of both knot theory and number theory, for instance knots in three manifolds versus primes in a number field, are compared throughout the book. These comparisons begin at an elementary level, slowly building up to advanced theories in later chapters. Definitions are carefully formulated and proofs are largely self-contained. When necessary, background information is provided and theory is accompanied with a number of useful examples and illustrations, making this a useful text for both undergraduates and graduates in the field of knot theory, number theory and geometry.
Knots And Primes
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Author : Masanori Morishita
language : en
Publisher: Springer Nature
Release Date : 2024-05-27
Knots And Primes written by Masanori Morishita and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-27 with Mathematics categories.
This book provides a foundation for arithmetic topology, a new branch of mathematics that investigates the analogies between the topology of knots, 3-manifolds, and the arithmetic of number fields. Arithmetic topology is now becoming a powerful guiding principle and driving force to obtain parallel results and new insights between 3-dimensional geometry and number theory. After an informative introduction to Gauss' work, in which arithmetic topology originated, the text reviews a background from both topology and number theory. The analogy between knots in 3-manifolds and primes in number rings, the founding principle of the subject, is based on the étale topological interpretation of primes and number rings. On the basis of this principle, the text explores systematically intimate analogies and parallel results of various concepts and theories between 3-dimensional topology and number theory. The presentation of these analogies begins at an elementary level, gradually building to advanced theories in later chapters. Many results presented here are new and original. References are clearly provided if necessary, and many examples and illustrations are included. Some useful problems are also given for future research. All these components make the book useful for graduate students and researchers in number theory, low dimensional topology, and geometry. This second edition is a corrected and enlarged version of the original one. Misprints and mistakes in the first edition are corrected, references are updated, and some expositions are improved. Because of the remarkable developments in arithmetic topology after the publication of the first edition, the present edition includes two new chapters. One is concerned with idelic class field theory for 3-manifolds and number fields. The other deals with topological and arithmetic Dijkgraaf–Witten theory, which supports a new bridge between arithmetic topology and mathematical physics.
The Knot Book
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Author : Colin Conrad Adams
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
The Knot Book written by Colin Conrad Adams and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.
Primes And Knots
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Author : Toshitake Kohno
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Primes And Knots written by Toshitake Kohno and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This volume deals systematically with connections between algebraic number theory and low-dimensional topology. Of particular note are various inspiring interactions between number theory and low-dimensional topology discussed in most papers in this volume. For example, quite interesting are the use of arithmetic methods in knot theory and the use of topological methods in Galois theory. Also, expository papers in both number theory and topology included in the volume can help a wide group of readers to understand both fields as well as the interesting analogies and relations that bring them together.
Knots And Links
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Author : Dale Rolfsen
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Knots And Links written by Dale Rolfsen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers 'practical' training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements.It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds. Other key books of interest on this topic available from the AMS are ""The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes"" and ""The Knot Book.""
Intelligence Of Low Dimensional Topology 2006
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Author : J. Scott Carter
language : en
Publisher: World Scientific
Release Date : 2007
Intelligence Of Low Dimensional Topology 2006 written by J. Scott Carter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This volume gathers the contributions from the international conference Intelligence of Low Dimensional Topology 2006, which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.
Knots Mathematics With A Twist
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Author : Alexei Sossinky
language : en
Publisher:
Release Date :
Knots Mathematics With A Twist written by Alexei Sossinky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Intelligence Of Low Dimensional Topology 2006
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Author : J Scott Carter
language : en
Publisher: World Scientific
Release Date : 2007-05-29
Intelligence Of Low Dimensional Topology 2006 written by J Scott Carter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-29 with Mathematics categories.
This volume gathers the contributions from the international conference “Intelligence of Low Dimensional Topology 2006,” which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.
Knots And Links
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Author : Peter R. Cromwell
language : en
Publisher: Cambridge University Press
Release Date : 2004-10-14
Knots And Links written by Peter R. Cromwell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-14 with Mathematics categories.
A richly illustrated 2004 textbook on knot theory; minimal prerequisites but modern in style and content.
Galois Theory And Modular Forms
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Author : Ki-ichiro Hashimoto
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Galois Theory And Modular Forms written by Ki-ichiro Hashimoto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
This volume is an outgrowth of the research project "The Inverse Ga lois Problem and its Application to Number Theory" which was carried out in three academic years from 1999 to 2001 with the support of the Grant-in-Aid for Scientific Research (B) (1) No. 11440013. In September, 2001, an international conference "Galois Theory and Modular Forms" was held at Tokyo Metropolitan University after some preparatory work shops and symposia in previous years. The title of this book came from that of the conference, and the authors were participants of those meet All of the articles here were critically refereed by experts. Some of ings. these articles give well prepared surveys on branches of research areas, and many articles aim to bear the latest research results accompanied with carefully written expository introductions. When we started our re~earch project, we picked up three areas to investigate under the key word "Galois groups"; namely, "generic poly nomials" to be applied to number theory, "Galois coverings of algebraic curves" to study new type of representations of absolute Galois groups, and explicitly described "Shimura varieties" to understand well the Ga lois structures of some interesting polynomials including Brumer's sextic for the alternating group of degree 5. The topics of the articles in this volume are widely spread as a result. At a first glance, some readers may think this book somewhat unfocussed.