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Dihedral Knot Projections and Their Associated Knots and Links
by
Paul Lopata
Laboratory for Physical Sciences
I introduce a two-parameter family of geometric figures that serve well as knot projections. These figures, referred to as dihedral knot projections (on account of their symmetries), are used to generate knot and link diagrams in a straightforward manner. In this talk, I describe these dihedral knot projections and their associated knots and links, and discuss some of their more interesting properties. Of particular note are the alternating knots formed in this way. I demonstrate that, given any two non-trivial alternating knots generated using this method, these two knots are distinct if and only if their corresponding dihedral knot projections are distinct (up to chirality).
Date received: December 17, 2018
Copyright © 2018 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbpq-31.