Knots And Primes

Author : Masanori Morishita
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 48,8 Mb
Release : 2011-11-27
Category : Mathematics
ISBN : 9781447121589

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Knots and Primes by Masanori Morishita Pdf

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. ​

Author : Toshitake Kohno
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 45,8 Mb
Release : 2006
Category : Algebraic number theory
ISBN : 9780821834565

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Primes and Knots by Toshitake Kohno Pdf

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.

Author : Colin Conrad Adams
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 50,9 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821836781

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The Knot Book by Colin Conrad Adams Pdf

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.

Author : Peter R. Cromwell
Publisher : Cambridge University Press
Page : 356 pages
File Size : 46,7 Mb
Release : 2004-10-14
Category : Mathematics
ISBN : 0521548314

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Knots and Links by Peter R. Cromwell Pdf

A richly illustrated 2004 textbook on knot theory; minimal prerequisites but modern in style and content.

Author : Charles Livingston
Publisher : Cambridge University Press
Page : 276 pages
File Size : 52,8 Mb
Release : 1993
Category : Mathematics
ISBN : 0883850273

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Knot Theory by Charles Livingston Pdf

This book uses only linear algebra and basic group theory to study the properties of knots.

Author : Masanori Morishita
Publisher : Springer Nature
Page : 268 pages
File Size : 50,5 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 9789819992553

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Knots and Primes by Masanori Morishita Pdf

Author : Gerhard Burde,Heiner Zieschang,Michael Heusener
Publisher : Walter de Gruyter
Page : 432 pages
File Size : 42,7 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9783110270785

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Knots by Gerhard Burde,Heiner Zieschang,Michael Heusener Pdf

This 3. edition is an introduction to classical knot theory. It contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory. Most of the topics considered in the book are developed in detail; only the main properties of fundamental groups and some basic results of combinatorial group theory are assumed to be known.

Author : Dale Rolfsen
Publisher : American Mathematical Soc.
Page : 458 pages
File Size : 50,9 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821834367

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Knots and Links by Dale Rolfsen Pdf

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.""

Author : Eric W. Weisstein
Publisher : CRC Press
Page : 3253 pages
File Size : 55,8 Mb
Release : 2002-12-12
Category : Mathematics
ISBN : 9781420035223

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CRC Concise Encyclopedia of Mathematics by Eric W. Weisstein Pdf

Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d

Author : J. Scott Carter
Publisher : World Scientific
Page : 398 pages
File Size : 42,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812770967

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Intelligence of Low Dimensional Topology 2006 by J. Scott Carter Pdf

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.

Author : Ki-ichiro Hashimoto,Katsuya Miyake,Hiroaki Nakamura
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 48,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302490

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Galois Theory and Modular Forms by Ki-ichiro Hashimoto,Katsuya Miyake,Hiroaki Nakamura Pdf

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.

Author : A. B. Sossinsky
Publisher : American Mathematical Society
Page : 149 pages
File Size : 45,6 Mb
Release : 2023-05-22
Category : Mathematics
ISBN : 9781470471514

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Knots, Links and Their Invariants by A. B. Sossinsky Pdf

This book is an elementary introduction to knot theory. Unlike many other books on knot theory, this book has practically no prerequisites; it requires only basic plane and spatial Euclidean geometry but no knowledge of topology or group theory. It contains the first elementary proof of the existence of the Alexander polynomial of a knot or a link based on the Conway axioms, particularly the Conway skein relation. The book also contains an elementary exposition of the Jones polynomial, HOMFLY polynomial and Vassiliev knot invariants constructed using the Kontsevich integral. Additionally, there is a lecture introducing the braid group and shows its connection with knots and links. Other important features of the book are the large number of original illustrations, numerous exercises and the absence of any references in the first eleven lectures. The last two lectures differ from the first eleven: they comprise a sketch of non-elementary topics and a brief history of the subject, including many references.

Author : Tristin Cleveland
Publisher : Scientific e-Resources
Page : 328 pages
File Size : 55,7 Mb
Release : 2018-04-11
Category : Electronic
ISBN : 9781839473265

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Number Theory by Tristin Cleveland Pdf

In spite of the fact that arithmetic majors are generally familiar with number hypothesis when they have finished a course in conceptual polynomial math, different students, particularly those in training and the human sciences, regularly require a more essential prologue to the theme. In this book the writer takes care of the issue of keeping up the enthusiasm of understudies at the two levels by offering a combinatorial way to deal with basic number hypothesis. In concentrate number hypothesis from such a point of view, arithmetic majors are saved reiteration and furnished with new bits of knowledge, while different understudies advantage from the subsequent effortlessness of the verifications for some hypotheses. Of specific significance in this content is the creator's accentuation on the estimation of numerical cases in number hypothesis and the part of PCs in getting such illustrations. The point of this book is to acquaint the reader with essential subjects in number hypothesis: hypothesis of distinctness, arithmetrical capacities, prime numbers, geometry of numbers, added substance number hypothesis, probabilistic number hypothesis, hypothesis of Diophantine approximations and logarithmic number hypothesis.

Author : Alekseĭ Bronislavovich Sosinskiĭ
Publisher : Harvard University Press
Page : 158 pages
File Size : 49,7 Mb
Release : 2002
Category : Mathematics
ISBN : 0674009444

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Knots by Alekseĭ Bronislavovich Sosinskiĭ Pdf

This book, written by a mathematician known for his own work on knot theory, is a clear, concise, and engaging introduction to this complicated subject, and a guide to the basic ideas and applications of knot theory. 63 illustrations.

Author : Chris Nunn
Publisher : Routledge
Page : 140 pages
File Size : 41,8 Mb
Release : 2015-10-16
Category : Psychology
ISBN : 9781317410072

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New Directions in Consciousness Studies by Chris Nunn Pdf

New Directions in Consciousness Studies describes a range of fresh ideas which promise to significantly advance scientific understanding of human nature. Written in non-specialized language, the book draws upon concepts and research from history, philosophy, neuroscience and physics to delineate new approaches to the study of consciousness. Early chapters deal with a range of ideas about our nature, and suggest that mind can usefully be viewed as a type of dynamic landscape. The account shows how our minds relate to their societies, brains and bodies and how they differ from computers. Later chapters develop a theory of the basis of consciousness (SoS theory). Using the physical concept of ‘broken symmetry’ the author shows how conscious mind may be rooted in temporality; a view that is supported by the occurrence of a wide range of anomalous phenomena. Potentially valuable future lines of research are identified. This is a unique and engaging book that will appeal to students and academics in the field of consciousness studies and other readers with an interest in consciousness.