On certain fibred ribbon disc pairs

Abstract

We prove that for any free group automorphism ϕ ∗ {\phi ^{\ast }} having a specified form there exists an invertible ribbon disc pair ( B 4 , D 2 ) ({B^4},\,{D^2}) such that the closure of B 4 − nbd ⁡ ( D 2 ) {B_4} - \operatorname {nbd} ({D^2}) fibres over the circle with fibre a handlebody and monodromy equal to ϕ ∗ {\phi ^{\ast }} . We apply this to obtain results about ribbon 1 1 - and 2 2 -knots.