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Junior Topology
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Ceren Kose, Zoom: On amphichirality of symmetric unions
Wednesday, October 13, 2021, 02:00pm - 03:00pm
Symmetric unions are an interesting class of knots. Although they have not been studied much for their own sake, they frequently appear in the literature. One such instance regards the question of whether there is a nontrivial knot with trivial Jones polynomial. Tanaka proposes a way of constructing symmetric unions such that if any are amphichiral, then they would have trivial Jones polynomial. In my talk, however, I will show that they are in fact trivial. Then I will discuss experimental data suggesting that amphichiral symmetric unions admit a certain form. The knots proposed by Tanaka are indeed not in this form, supporting the observation. I will end by further confirming this observation for the simplest type of symmetric unions.
Location: Zoom

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