Equivariant algebraic concordance of strongly invertible knots

By considering a particular type of invariant Seifert surfaces we define a homomorphism Phi from the (topological) equivariant concordance group of directed strongly invertible knots to a new equivariant algebraic concordance group. We prove that Phi lifts both Miller and Powell's equivariant algebraic concordance homomorphism, and Alfieri and Boyle's equivariant signature. Moreover, we provide a partial result on the isomorphism type of this equivariant algebraic concordance group, and we obtain a new obstruction to equivariant sliceness, which can be viewed as an equivariant Fox-Milnor condition. We define new equivariant signatures and using these we obtain novel lower bounds on the equivariant slice genus. Finally, we show that Phi can obstruct equivariant sliceness for knots with Alexander polynomial one.