2022/03/07 by Ryoto Tange, Tange, Ryoto, Jun Ueki +1
Mathematics · Medicine · #11R23 #11S99 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Ophthalmology and Eye Disorders #Primary 57K10 #Secondary 57M10
paper · pdf · doi:10.48550/arxiv.2203.03239
openalex publication_date 2022/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let p be a prime number and m an integer coprime to p. In the spirit of arithmetic topology, we introduce the notions of the twisted Iwasawa invariants λ, μ, ν of \rm GLN-representations and ℤ/mℤ× ℤp-covers of knots. We prove among other things that the set of Iwasawa invariants determine the genus and the fiberedness of a knot, yielding their profinite rigidity. Several intuitive examples are attached. We further prove the μ=0 theorem for \rm SL2-representations of twist knot groups and give some remarks.