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• Berglund, M
• Cantarella, J
• Casey, M
• Dannenberg, E
• George, W
• Johnson, A
• Kelley, A
• LaPointe, A
• Mastin, M
• Parsley, J
• Rooney, J
• Whitaker, R
• [+] on Google Scholar
• Berglund, M
• Cantarella, J
• Casey, M
• Dannenberg, E
• George, W
• Johnson, A
• Kelley, A
• LaPointe, A
• Mastin, M
• Parsley, J
• Rooney, J
• Whitaker, R
• [+] on PubMed
• Berglund, M
• Cantarella, J
• Casey, M
• Dannenberg, E
• George, W
• Johnson, A
• Kelley, A
• LaPointe, A
• Mastin, M
• Parsley, J
• Rooney, J
• Whitaker, R

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Symmetry 2012, 4(1), 143-207; doi:10.3390/sym4010143

Article

Intrinsic Symmetry Groups of Links with 8 and Fewer Crossings

Michael Berglund ¹ , Jason Cantarella ^1,* , Meredith Perrie Casey ¹ , Eleanor Dannenberg ¹ , Whitney George ¹ , Aja Johnson ¹ , Amelia Kelley ¹ , Al LaPointe ¹ , Matt Mastin ¹ , Jason Parsley ² , Jacob Rooney ¹  and Rachel Whitaker ¹

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; 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 Full-Text [1600 KB, uploaded 20 February 2012 10:01 CET]

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

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