The theme of the present book is the analogy between knot theory and number theory,
based on the homotopical analogies between knots and primes, 3-manifolds and number …

We study a topological analogue of idèlic class field theory for 3-manifolds in the spirit of
arithmetic topology. We first introduce the notion of a very admissible link $\mathcal {K} $ in …

We refine McMullen's construction of sequences of knots in $ S^ 3$ obeying the Chebotarev
law in two ways. One is to extend his theorem for generalized pseudo-Anosov flows, which …

É. Ghys proved that the linking numbers of modular knots and the “missing” trefoil K 2, 3 in S
3 coincide with the values of a highly ubiquitous function called the Rademacher symbol for …

Let pp be a prime number and mm an integer coprime to p p. In the spirit of arithmetic
topology, we introduce the notions of the twisted Iwasawa invariants λ, μ, ν λ,μ,ν of GL N …

This chapter explores the implementation and effectiveness of statistical diagnostics systems
for monitoring and diagnosing electrical equipment (EE) components using information …

Based on our homological idelic class field theory, we formulate an analogue of the Hilbert
reciprocity law on a rational homology 3-sphere endowed with an infinite link, in the spirit of …

This thesis consists of two chapters except for this chapter. Chapter 2 gives a new approach
to Weber's class number problem that asks whether specific infinitely many number fields …

Idelic class field theory describes Abelian extensions of a number field k in terms of the
idèles of k. Firstly, we construct local class field theory for the local field at each prime of k …