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Universitext

Knots and Primes

An Introduction to Arithmetic Topology

Authors: Morishita, Masanori

  • Starts at an elementary level and builds up to a more advanced theoretical discussion
  • Written by a world expert on arithmetic topology
  • A large number of illustrative examples are provided throughout​
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eBook 20,22 €
41,64 € (listprice)
price for Spain (gross)
valid through June 30, 2017
  • ISBN 978-1-4471-2158-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 25,99 €
51,95 € (listprice)
price for Spain (gross)
valid through June 30, 2017
  • ISBN 978-1-4471-2157-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

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. ​

Reviews

“This is one of the best textbook I have seen in the last few years. … this books is amazing! I really enjoyed it and I hope you will also enjoy it. It definitely should be part of your library if you work in number theory and/or topology. This book will become a classical very soon!” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, June, 2016)

“The book under review is the first systematic treatment of the subject in a format suitable for a textbook. … The book is rich in material for anybody interested in either the arithmetic or the topological side, and the connections and interactions are presented in a very convincing and detailed way.” (Matilde Marcolli, Mathematical Reviews, March, 2013)

“Once you’ve lived long enough in mathematics, the themes addressed in Knots and Primes: An Introduction to Arithmetic Topology are both familiar and exceedingly attractive. This is a fascinating topic … and Morishita’s book is an important contribution. … it will spur a lot of work in this beatiful and accessible area of contemporary mathematics.” (Michael Berg, The Mathematical Association of America, May, 2012)


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Table of contents (14 chapters)

  • Introduction

    Morishita, Masanori

    Pages 1-7

    Preview Buy Chapter 30,19 €
  • Preliminaries—Fundamental Groups and Galois Groups

    Morishita, Masanori

    Pages 9-48

    Preview Buy Chapter 30,19 €
  • Knots and Primes, 3-Manifolds and Number Rings

    Morishita, Masanori

    Pages 49-53

    Preview Buy Chapter 30,19 €
  • Linking Numbers and Legendre Symbols

    Morishita, Masanori

    Pages 55-60

    Preview Buy Chapter 30,19 €
  • Decompositions of Knots and Primes

    Morishita, Masanori

    Pages 61-68

    Preview Buy Chapter 30,19 €

Buy this book

eBook 20,22 €
41,64 € (listprice)
price for Spain (gross)
valid through June 30, 2017
  • ISBN 978-1-4471-2158-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 25,99 €
51,95 € (listprice)
price for Spain (gross)
valid through June 30, 2017
  • ISBN 978-1-4471-2157-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Knots and Primes
Book Subtitle
An Introduction to Arithmetic Topology
Authors
Series Title
Universitext
Copyright
2012
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-1-4471-2158-9
DOI
10.1007/978-1-4471-2158-9
Softcover ISBN
978-1-4471-2157-2
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XI, 191
Number of Illustrations and Tables
42 b/w illustrations
Additional Information
English Language edition of 'Musubime to Sosu' Copyright © Springer Japan 2009
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