Twisted Iwasawa invariants of knots

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 lambda,mu,nu$\lambda , \mu , \nu$ of GLN-representations and Z/mZxZp${\mathbb {Z}}/m{\mathbb {Z}}\times {\mathbb {Z}}_{p}$-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 mu=0$\mu =0$ theorem for SL2-representations of twist knot groups and give some remarks.