2024/01/06 by Sohei Tateno, Tateno, Sohei, Jun Ueki +1
Mathematics · #11R23 #11R29 #20E18 #57M10 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Primary 57M12 #Secondary 57K10
paper · pdf · doi:10.48550/arxiv.2401.03258
openalex publication_date 2024/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Let p be a prime number and let d∈ ℤ>0. In this paper, following the analogy between knots and primes, we study the p-torsion growth in a compatible system of (ℤ/pnℤ)d-covers of 3-manifolds and establish several analogues of Cuoco--Monsky's multivariable versions of Iwasawa's class number formula. Our main goal is to establish the Cuoco--Monsky type formula for branched covers of links in rational homology 3-spheres. In addition, we prove the precise formula over integral homology 3-spheres prompted by Greenberg's conjecture. We also derive results on reduced Alexander polynomials and on the Betti number periodicity. Furthermore, we investigate the twisted Whitehead links in S3 and point out that the Iwasawa μ-invariant of a ℤp 2-cover can be an arbitrary non-negative integer. We also calculate the Iwasawa μ and λ-invariants of the Alexander polynomials of all links in Rolfsen's table.