Titlebook: Knots and Primes; An Introduction to A Masanori Morishita Textbook 2024Latest edition The Editor(s) (if applicable) and The Author(s), unde

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Knots and Primes, 3-Manifolds and Number Rings,In this chapter we explain the basic analogies between knots and primes, 3-manifolds and number rings, which will be fundamental in subsequent chapters.

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Linking Numbers and Legendre Symbols,In this chapter, we shall discuss the analogy between the linking number and the Legendre symbol, based on the analogies between knots and primes in Chap. ..

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Decompositions of Knots and Primes,As we have seen in Sect. ., the Legendre symbol describes how a prime number is decomposed in a quadratic extension.

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Link Groups and Galois Groups with Restricted Ramification,As explained in Chap. ., our basic idea is to regard a Galois group with restricted ramification ., ., as an analogue of a link group . (cf. (.)).

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