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The 27 Possible Intrinsic Symmetry Groups of Two-Component Links
Symmetry 2012, 4(1), 143-207; doi:10.3390/sym4010143

Intrinsic Symmetry Groups of Links with 8 and Fewer Crossings

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1 University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA 2 Wake Forest University, Mathematics Department, PO Box 7388, Winston-Salem, NC 27109, USA
* Author to whom correspondence should be addressed.
Received: 4 January 2012 / Revised: 18 January 2012 / Accepted: 31 January 2012 / Published: 20 February 2012
(This article belongs to the Special Issue Symmetry and Beauty of Knots)
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We present an elementary derivation of the “intrinsic” symmetry groups for links of 8 or fewer crossings. We show that standard invariants are enough to rule out all potential symmetries outside the symmetry group of the group of the link for all but one of these links and present explicit isotopies generating the symmetry group for every link.
Keywords: knot; symmetry group of knot; link symmetry; Whitten group knot; symmetry group of knot; link symmetry; Whitten group
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Berglund, M.; Cantarella, J.; Casey, M.P.; Dannenberg, E.; George, W.; Johnson, A.; Kelley, A.; LaPointe, A.; Mastin, M.; Parsley, J.; Rooney, J.; Whitaker, R. Intrinsic Symmetry Groups of Links with 8 and Fewer Crossings. Symmetry 2012, 4, 143-207.

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