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2012 | OriginalPaper | Chapter

3. Knots and Primes, 3-Manifolds and Number Rings

Author : Masanori Morishita

Published in: Knots and Primes

Publisher: Springer London

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Abstract

In this chapter we explain the basic analogies between knots and primes, 3-manifolds and number rings and present a dictionary of these analogies, which will be fundamental and used throughout subsequent chapters.

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previous chapter Preliminaries—Fundamental Groups and Galois Groups
next chapter Linking Numbers and Legendre Symbols
Footnotes
1
Although we should write \(G_{\{ \mathfrak{p}\}}, D_{\{ \mathfrak{p}\}}\) and \(I_{\{\mathfrak{p}\}}\) as analogues of G K , D K and I K respectively, we often write \(G_{\mathfrak{p}}, D_{\mathfrak{p}}\) and \(I_{\mathfrak{p}}\) for simplicity. For a prime number p, we also write G {p},D {p} and I {p} or simply G p ,D p and I p for G {(p)},D {(p)} and I {(p)}, respectively.
 
Literature
[Dn1]
Deninger, C.: Some analogies between number theory and dynamical systems on foliated spaces. Doc. Math. J. DMV. Extra Volume ICM I, 23–46 (1998)
[Dn2]
Deninger, C.: A note on arithmetic topology and dynamical systems. In: Algebraic Number Theory and Algebraic Geometry. Contemporary Mathematics, vol. 300, pp. 99–114. Am. Math. Soc., Providence (2002)
[GL]
[Iw1]
Iwasawa, K.: On a certain analogy between algebraic number fields and function fields. Sūgaku 15, 65–67 (1963) (in Japanese) MathSciNetMATH
[Mn2]
Morin, B.: Sur le topos Weil-étale d’un corps de nombres. Thèse, Université Bordeaux I (2008)
[NSW]
Neukirch, J., Schmidt, A., Wingberg, K.: Cohomology of Number Fields, 2nd edn. Grundlehren der Mathematischen Wissenschaften, vol. 323. Springer, Berlin (2008) MATH
[Ra]
Ramachandran, N.: A note on arithmetic topology. C. R. Math. Acad. Sci. Soc. R. Can. 23(4), 130–135 (2001) MathSciNetMATH
[Sn]
Sunada, T.: Fundamental Groups and Laplacians. Kinokuniya, Tokyo (1988) (in Japanese)
[Wh]
Metadata
Title
Knots and Primes, 3-Manifolds and Number Rings
Author
Masanori Morishita
Copyright Year
2012
Publisher
Springer London
Book
Knots and Primes

Print ISBN: 978-1-4471-2157-2

Electronic ISBN: 978-1-4471-2158-9

Copyright Year: 2012

DOI
https://doi.org/10.1007/978-1-4471-2158-9_3

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