Twisted Iwasawa invariants of knots

Abstract

AbstractLet 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 of GLN‐representations and ‐covers of knots. We prove among other things that the set of Iwasawa invariants determines the genus and the fiberedness of a knot, yielding their profinite rigidity. Several intuitive examples are attached. We further prove the theorem for SL2‐representations of twist knot groups and give some remarks.