2023/03/21 by Di Prisa, Alessio
#57K10 (Primary) #57M60 #57R85 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2303.11895
By considering a particular type of invariant Seifert surfaces we define a homomorphism Φ from the (topological) equivariant concordance group of directed strongly invertible knots \widetildeC to a new equivariant algebraic concordance group \widetildeGℤ. We prove that Φ 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 \widetildeGℤ, 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 Φ can obstruct equivariant sliceness for knots with Alexander polynomial one.