Primes-knots dictionary, see Morin thesis.
http://www.neverendingbooks.org/index.php/what-is-the-knot-associated-to-a-prime.html
http://mathoverflow.net/questions/50879/what-is-the-knot-associated-to-a-prime
http://www.neverendingbooks.org/index.php/who-dreamed-up-the-primesknots-analogy.html
http://mathoverflow.net/questions/4075/questions-about-analogy-between-spec-z-and-3-manifolds
http://mathoverflow.net/questions/31250/prime-numbers-as-knots-alexander-polynomial
There is a CONM volume on primes and knots.
arXiv:1204.4892 On the Iwasawa invariants of a link in the 3-sphere from arXiv Front: math.NT by Teruhisa Kadokami, Yasushi Mizusawa Based on the analogy between knots and primes, J. Hillman, D. Matei and M. Morishita defined the Iwasawa invariants for sequences of cyclic covers of links with an analogue of Iwasawa’s class number formula of number fields. In this paper, we consider the existence of covers of links with prescribed Iwasawa invariants, discussing analogies in number theory. We also propose and consider a problem analogous to Greenberg’s conjecture.
nLab page on Arithmetic topology