Eisermann and Lamm introduced a notion of symmetric equivalence among symmetric union diagrams and studied it using a refined form of the Jones polynomial. We introduced invariants of symmetric equivalence via refined versions of topological spin models and provided a partial answer to a question left open by Eisermann and Lamm. In this paper we adopt a new approach to the symmetric equivalence problem and give a complete answer to the original question left open by Eisermann and Lamm.
The second author was partially supported by the MIUR-PRIN project 2017JZ2SW5.
"On symmetric equivalence of symmetric union diagrams." Osaka J. Math. 58 (4) 755 - 765, October 2021.