Self-Dual Maps II: Links and Symmetry

In this paper, we investigate representations of links that are either centrally symmetric in R ³ or antipodally symmetric in S ³. By using the notions of antipodally self-dual and antipodally symmetric maps, introduced and studied by the authors in [L. Montejano, J. L. Ram-Irez Alfons In, and I. Rasskin, SIAM J. Discrete Math., 36 (2022), pp. 1551-1566], we are able to present sufficient combinatorial conditions for a link L to admit such representations. The latter naturally provide sufficient conditions for L to be amphichiral. We also introduce another (closely related) method yielding again sufficient conditions for L to be amphichiral. We finally prove that a link L, associated to a map G, is amphichiral if the self-dual pairing of G is not one of 6 specific cases among the classification of the 24 self-dual pairing Cor(G) ► Aut(G).