2019 Student Research Conference:
32nd Annual Student Research Conference

Multi-Skein Invariants for Welded and Extended Welded Knots and Links

Timothy A. Leafblad
Prof. Tony Vazzana, Faculty Mentor

In the mathematical theory of knots, knot invariants, which are tools for distinguishing among various knots, are of particular interest. Many invariants of classical knots (formalized as embeddings of the circle into R^3) are known. Skein-theoretic approaches to building knot invariants most commonly consist of two primary components: a skein relation, which allows for the construction of a polynomial in the process of decomposing a knot; and a collection of constraints on the coefficients of the chosen skein relation that guarantees that the defined polynomial is an invariant. We employ a skein-theoretic approach to obtain invariants of new extensions of classical knots known as extended welded knots.

Keywords: knot invariant, skein relation, virtual knots, extended welded knots, Reidemeister moves, wen mark


Presentation Type: Oral Paper

Session: 203-6
Location: BH 212
Time: 11:30

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