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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Homology Groups and Ideal Class Groups II: Higher-Order Genus Theory,Let . be a rational homology 3-sphere which is a double covering of . ramified over a .-component link and let . be a quadratic extension of . ramified over . odd prime numbers.

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Homology Groups and Ideal Class Groups III: Asymptotic Formulas,As we discussed in Chap. ., there is a group-theoretic analogy between the knot module associated to the infinite cyclic covering of a knot exterior and the Iwasawa module associated to the cyclotomic .-extension of number fields. Based on this analogy, there are found close parallels between the Alexander–Fox theory and Iwasawa theory.

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Torsions and the Iwasawa Main Conjecture,The Iwasawa main conjecture asserts that the Iwasawa polynomial coincides essentially with the Kubota–Leopoldt .-adic analytic zeta function.

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Moduli Spaces of Representations of Knot and Prime Groups,In view of the analogy between a knot group . and a prime group ., we expect some analogies between the moduli spaces of representations of knot and prime groups.

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Deformations of Hyperbolic Structures and ,-Adic Ordinary Modular Forms,As we have seen in Chap. ., the Alexander–Fox theory and Iwasawa theory may be regarded as theories on the moduli spaces of 1-dimensional representations.

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https://doi.org/10.1007/978-981-99-9255-33-manifolds; arithmetic topology; homology groups; knots and primes; legendre symbols; number rings

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Preliminaries: Fundamental Groups and Galois Groups,summary of fundamental groups and Galois theory for topological spaces and arithmetic rings in Sects. 2.1 and 2.2, since the analogies between topological and arithmetic fundamental/Galois groups are fundamental in this book.

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Masanori MorishitaIs the new, updated edition of the first book on arithmetic topology.Provides a solid foundation of arithmetic topology for graduate students and researchers.Includes useful problems guiding future st

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