Vol. 9, No. 2, 2016

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Klein links and related torus links

Enrique Alvarado, Steven Beres, Vesta Coufal, Kaia Hlavacek, Joel Pereira and Brandon Reeves

Vol. 9 (2016), No. 2, 347–359
Abstract

In this paper, we present our constructions and results leading up to our discovery of a class of Klein links that are not equivalent to any torus links. In particular, we calculate the number and types of components in a Kp,q Klein link and show that Kp,p Kp,p1, Kp,2 Tp1,2, and K2p,2p T2p,p. Finally, we show that in contrast to the fact that every Klein knot is a torus knot, no Klein link Kp,p, where p 5 is odd, is equivalent to a torus link.

Keywords
knot theory, Klein links, torus links
Mathematical Subject Classification 2010
Primary: 57M25
Milestones
Received: 3 January 2015
Revised: 23 February 2015
Accepted: 26 February 2015
Published: 2 March 2016

Communicated by Colin Adams
Authors
Enrique Alvarado
Department of Mathematics
Washington State University
Pullman, WA 99164
United States
Steven Beres
Department of Mathematics
Gonzaga University
Spokane, WA 99258
United States
Vesta Coufal
Department of Mathematics
Gonzaga University
Spokane, WA 99258
United States
Kaia Hlavacek
Department of Mathematics
Gonzaga University
Spokane, WA 99258
United States
Joel Pereira
Department of Mathematics
Gonzaga University
Spokane, WA 99258
United States
Brandon Reeves
Department of Economics
University of Wisconsin
Madison, WI 53706
United States