Abstract
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. 3, we give a topological analogue of Hilbert theory for a finite Galois covering of 3-manifolds.
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References
Hilbert, D.: Die Theorie der algebraischen Zahlkörper. Jahresber. Dtsch. Math.-Ver. 4, 175–546 (1897). In: Gesammelte Abhandlungen. Band I: Zahlentheorie, 2nd edn. Springer, Berlin (1970) (in German)
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Morishita, M. (2012). Decompositions of Knots and Primes. In: Knots and Primes. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-2158-9_5
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DOI: https://doi.org/10.1007/978-1-4471-2158-9_5
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2157-2
Online ISBN: 978-1-4471-2158-9
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