Equivariant unknotting numbers of strongly invertible knots

Abstract

We study symmetric crossing change operations for strongly invertible knots. Our main theorem is that the most natural notion of equivariant unknotting number is not additive under connected sum, in contrast with the longstanding conjecture that unknotting number is additive.

Added a computation of the total equivariant unknotting numbers for torus knots. We show that a minimal length unknotting sequence can be made equivariant