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

Intrinsic Symmetry Groups of Links with 8 and Fewer Crossings

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Received: 4 January 2012; in revised form: 18 January 2012 / Accepted: 31 January 2012 / Published: 20 February 2012
(This article belongs to the Special Issue Symmetry and Beauty of Knots)
Download PDF [1600 KB, uploaded 20 February 2012]
Abstract: 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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MDPI and ACS Style

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.

AMA Style

Berglund M, Cantarella J, Casey MP, 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(1):143-207.

Chicago/Turabian Style

Berglund, Michael; Cantarella, Jason; Casey, Meredith Perrie; Dannenberg, Eleanor; George, Whitney; Johnson, Aja; Kelley, Amelia; LaPointe, Al; Mastin, Matt; Parsley, Jason; Rooney, Jacob; Whitaker, Rachel. 2012. "Intrinsic Symmetry Groups of Links with 8 and Fewer Crossings." Symmetry 4, no. 1: 143-207.


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