arXiv subjects

Giovanni Framba

Publications and source records attributed to Giovanni Framba.

3 recordsLinked to original sources

arXiv2026

Equivariant Grid Homology for Strongly Invertible Knots

We study an equivariant version of grid homology for strongly invertible knots. We consider symmetric grid diagrams encoding the strong inversion, prove that every strongly invertible knot admits such a representation, and establish the corresponding analogue of Cromwell's theorem. A symmetric grid induces an involution on the associated grid complex. We study the mapping cone of the sum of the identity and this involution, proving that its homology is an invariant of strongly invertible knots. Finally, we define equivariant analogues of the tau invariant and of the Legendrian grid invariants, and show that the former provide lower bounds for equivariant unknotting numbers and for the genus of simple equivariant cobordisms.

math.GT↗

arXiv2023

Solvability of concordance groups and Milnor invariants

Using Milnor invariants, we prove that the concordance group $\mathcal{C}(2)$ of $2$-string links is not solvable. As a consequence we prove that the equivariant concordance group of strongly invertible knots is also not solvable, and we answer a conjecture posed by Kuzbary.

math.GT↗

arXiv2023

A new invariant of equivariant concordance and results on 2-bridge knots

We study the equivariant concordance classes of two-bridge knots, providing an easy formula to compute their butterfly polynomial, and we give two different proofs that no two-bridge knot is equivariantly slice. Finally, we introduce a new invariant of equivariant concordance for strongly invertible knots. Using this invariant as an obstruction we strengthen the result on two-bridge knots, proving that their equivariant concordance order is always infinite.

math.GT↗