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Узлы и теория представлений
9 октября 2018 г. 18:30, г. Москва, ГЗ МГУ, ауд. 14-03

[Concordance invariants of virtual knots]

Ганс Боден

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Аннотация: This talk will focus on virtual knot concordance and is a based on joint work with Micah Chrisman and Robin Gaudreau. The goal is to extend classical concordance invariants to the virtual setting and apply them to determine sliceness and the 4-genus for low crossing virtual knots. One of the obstacles is the absence of Seifert surfaces for virtual knots, and for that reason we focus on the subclass of almost classical (AC) knots, which consist of virtual knots which can be represented as homologically trivial knots in thickened surfaces. Such knots admit Seifert surfaces, which can be used to define Seifert matrices, Alexander-like polynomials, signatures, and twisted signatures. For round AC knots, the resulting invariants will depend on the choice of Seifert surface, but for long virtual knots, they are independent. In either case, they give obstructions to slicing AC knots and we apply them to determine sliceness and 4-ball genus for AC knots up to 6 crossings. Parity projection, and the fact that it preserves virtual knot concordance, allows one to extend the invariants to all virtual knots.

Язык доклада: английский

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