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Invariants of Graphs and Delta-matroids Generating Knot Invariants

Student: Dunaykin Alexander

Supervisor: Sergei Lando

Faculty: Faculty of Mathematics

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2016

To a singular knot K with n double points, we can associate a chord diagram with n chords. A chord diagram can also be understood as a 4-regular graph endowed with an Euler circuit. To such data, a transition matroid is associated. In fact, the transition matroid depends only on the graph, not on the Euler circuit in it. For a given 4-regular graph we can build a transition polynomial. We specialize this polynomial to a multiplicative weight system, that is, a function on chord diagrams satisfying 4-term relations and determining a knot invariant.

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