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Educational Programme
Final Grade
Year of Graduation
Alexander Dunaykin
Invariants of Graphs and Delta-matroids Generating Knot Invariants
(Bachelor’s programme)
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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