• algebraic concordance
• equivariant signature
• equivariant concordance
• equivariantly slice knot
• strongly invertible knots
• knot concordance

The main subject of this thesis is the study of the equivariant concordance group of directed strongly invertible knots, introduced by Sakuma.

Considering a particular type of spanning surfaces for strongly invertible knots, we define a new invariant for equivariant concordance, namely a homomorphism from the equivariant concordance group to an equivariant version of the Witt group of the field of rational numbers.
Then, we investigate its relation with previously known invariants, and in particular we show that from this invariant one can naturally retrieve an equivariant version of the knot signature for strongly invertible knots, defined recently by Alfieri, Boyle and Issa.

Finally, we prove that the equivariant concordance group is not abelian, by exhibiting an infinite family of nontrivial commutators, answering a conjecture attributed to Sakuma.