Intrinsic Symmetry Groups of Links with 8 and Fewer Crossings

We present new computations of “intrinsic” symmetry groups for knots and links of 8 or fewer crossings. The standard symmetry group for a link is the mapping class group MCG(S, L) or Sym(L) of the pair (S, L). Elements in this symmetry group can (and often do) fix the link and act nontrivially only on its complement. We ignore such elements and focus on the “intrinsic” symmetry group of a link, defined to be the image Σ(L) of the natural homomorphism MCG(S, L) → MCG(S) × MCG(L). This different symmetry group, first defined by Whitten in 1969, records directly whether L is isotopic to a link L obtained from L by permuting components or reversing orientations. While the standard symmetry groups Sym(L) have been computed for knots of up to 10 crossings and most links with up to 9 crossings, we give here the first comprehensive tables of the groups Σ(L). CONTENTS List of Tables 2 List of Figures 2