Titlebook: Knots and Primes; An Introduction to A Masanori Morishita Textbook 20121st edition Springer-Verlag London Limited 2012 3-manifolds.arithmet

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Morsel

Torsions and the Iwasawa Main Conjecture, analytic zeta function. According to the analogy between the Iwasawa polynomial and the Alexander polynomial in Chap. ., we discuss geometric analogues of the Iwasawa main conjecture, namely, some relations between the Reidemeister–Milnor torsion and the Lefschetz or spectral zeta function.

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BARK

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audiologist

Decompositions of Knots and Primes,In this chapter we review Hilbert theory which deals with, in a group-theoretic manner, the decomposition of a prime in a finite Galois extension of number fields. Based on the analogies in Chap. ., we give a topological analogue of Hilbert theory for a finite Galois covering of 3-manifolds.

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notice

Link Groups and Galois Groups with Restricted Ramification,In this chapter we discuss the analogy between Galois groups with restricted ramification and link groups. In particular, we shall see the close analogy between Milnor’s theorem on the structure of a link group and a theorem by H. Koch on the structure of a pro-. Galois group over the rational number field with restricted ramification.

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Masanori MorishitaStarts 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?.