Geodesic
Topological Iwasawa invariants and arithmetic statistics
Documenta mathematica, Tome 27 (2022), pp. 1643-1669 Cet article a éte moissonné depuis la source EMS Press

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Given a prime number p, we study topological analogues of Iwasawa invariants associated to Zp​-covers of the 3-sphere that are branched along a link. We prove explicit criteria to detect these Iwasawa invariants, and apply them to the study of links consisting of 2 component knots. Fixing the prime p, we prove statistical results for the average behaviour of p-primary Iwasawa invariants for 2-bridge links that are in Schubert normal form. Our main result, which is entirely unconditional, shows that the density of 2-bridge links for which the μ-invariant vanishes, and the λ-invariant is equal to 1, is (1−p1​). We also conjecture that the density of 2-bridge links for which the μ-invariant vanishes is 1, and this is significantly backed by computational evidence. Our results are proven in a topological setting, yet have arithmetic significance, as we set out new directions in arithmetic statistics and arithmetic topology.
DOI : 10.4171/dm/x14
Classification : 11R23, 57K10, 57K14
Mots-clés : knot theory, arithmetic statistics, arithmetic topology, topological Iwasawa invariants, analogies between number theory and topology 
@article{10_4171_dm_x14,
     author = {Cedric Dion and Anwesh Ray},
     title = {Topological {Iwasawa} invariants and arithmetic statistics},
     journal = {Documenta mathematica},
     pages = {1643--1669},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/x14},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x14/}
}
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Cedric Dion; Anwesh Ray. Topological Iwasawa invariants and arithmetic statistics. Documenta mathematica, Tome 27 (2022), pp. 1643-1669. doi: 10.4171/dm/x14

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