Abstract
In this chapter we explain the basic analogies between knots and primes, 3-manifolds and number rings and present a dictionary of these analogies, which will be fundamental and used throughout subsequent chapters.
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Notes
- 1.
Although we should write \(G_{\{ \mathfrak{p}\}}, D_{\{ \mathfrak{p}\}}\) and \(I_{\{\mathfrak{p}\}}\) as analogues of G K , D K and I K respectively, we often write \(G_{\mathfrak{p}}, D_{\mathfrak{p}}\) and \(I_{\mathfrak{p}}\) for simplicity. For a prime number p, we also write G {p},D {p} and I {p} or simply G p ,D p and I p for G {(p)},D {(p)} and I {(p)}, respectively.
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Morishita, M. (2012). Knots and Primes, 3-Manifolds and Number Rings. In: Knots and Primes. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-2158-9_3
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DOI: https://doi.org/10.1007/978-1-4471-2158-9_3
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