Symmetries of nonelliptic Montesinos links

Square numbers and polynomial invariants of achiral knots

“…In [5], a weaker claim was left as an exercise, with the restriction to odd length knots. With a different small restriction (nonellipticity), the result was given in corollary 1.4 of [4]. However, the heavy machinery of Thurston's hyperbolization theorem is not needed, and a proof can be obtained (without restrictions) from the classification of Montesinos links.…”

Twisted Alexander polynomials of periodic knots

“…Note that all free periods for knots up to 10-crossings not settled by Hartley were determined by the combined works of Boileau and Zimmermann in [2] and Sakuma in [37]. In particular, it was shown in [2] that 10 62 is not freely periodic.…”

Intrinsic Symmetry Groups of Links with 8 and Fewer Crossings

“…Henry and Weeks [3,22] report Sym(L) groups for hyperbolic links up to 9 crossings, while Boileau and Zimmerman [4] computed Sym(L) groups for non-elliptic Montesinos links with up to 11 crossings, and Bonahon and Siebenmann computed Sym(L) for the Borromean rings link (6 Comparing all this data with ours, we see that Lemma 10.1 Among all links of 8 and fewer crossings with known Sym(L) groups, the Whitten symmetry group Σ(L) is not isomorphic to Sym(L) only for the links in Table 13. Table 13.…”

“…In the same year, Weeks and Henry used the program SnapPea to compute the symmetry groups for hyperbolic knots and links of 9 and fewer crossings [3]. These efforts followed earlier tabulations of symmetry groups by Boileau and Zimmermann [4], who found symmetry groups for non-elliptic Montesinos links with 11 or fewer crossings. We consider a different group of symmetries of a link L given by the image of the natural homomorphism π : Sym(L) = MCG(S 3 , L) → MCG(S 3 ) × MCG(L)…”