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Abstract

The (m,n)-Klein links are formed by altering the rectangular representation of an (m,n)-torus link. Using the braid representation of a (m,n)-Klein link, we generalize a previous braid word result and show that the (m, 2m)-Klein link can be expressed recursively. Applying braid permutations, we determine a formula for the number of components for an (m,n)-Klein link and classify the Klein links that are equivalent to knots.

Author Bio

David Freund graduated from The College of Wooster with a B.A. in Mathematics in May 2013. He is currently pursuing a Ph.D. in mathematics at Dartmouth College. The research was conducted in the summer of 2011 as part of the Applied Mathematics Research Experience (AMRE) program at the College of Wooster.

Sarah Smith-Polderman graduated from The College of Wooster with a B.A. in Mathematics in May 2013. She completed a M.Ed. at the University of Cincinnati in August 2014. The research was conducted in the summer of 2011 as part of the Applied Mathematics Research Experience (AMRE) program at The College of Wooster.

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