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Educational Programme
Final Grade
Year of Graduation
Alexander Dunaykin
Finite-order Invariants of Legendrian Knots
(Master’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 oriented Euler circuit. 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 thus a knot invari-

ant. A function on ribbon graphs satisfying 4-term relations defines an

invariant of links rather than of knots. However, the vector space freely

spanned by ribbon graphs isn’t a Hopf algebra. Nevertheless it could be

mapped to the Hoph algebra of binary delta-matroids. We extend our

function to ribbon graphs and further to binary delta-matroids and show

that 4-term relations are satisfied for it.

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