Algebraic concordance and strongly invertible knots

In 1969 Levine defined a surjective homomorphism from the knot concordance group to the so-called algebraic concordance group, which is a Witt group of Seifert forms. Studying symmetric knots and in particular strongly invertible knots, a natural question is whether it is possible to define an appropriate equivariant version of algebraic concordance. In this talk we briefly recall Levine's construction and we highlight some of the problems occurring when trying to define its equivariant analogous. Finally, we define a notion of equivariant algebraic concordance for strongly invertible knots and we show some of the differences with the classical case.