Year: 2024
Type: article
Abstract: By considering a particular type of invariant Seifert surfaces we define a homomorphism from the (topological) equivariant concordance group of directed strongly invertible knots to a new equivariant algebraic concordance group . We prove that lifts both Miller and Powell's equivariant algebraic concordance homomorphism (J. Lond. Math. Soc. (2023), no. 107, 2025‐2053) and Alfieri and Boyle's equivariant signature (Michigan Math. J. 1 (2023), no. 1, 1–17). Moreover, we provide a partial result on the isomorphism type of and 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 can obstruct equivariant sliceness for knots with Alexander polynomial one.
Source: Journal of Topology
DOI: 10.1112/topo.70006
Author: Alessio Di Prisa
Institution: Scuola Normale Superiore
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,780
OpenAlex ID: W4404330456