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Finite-order Invariants of Legendrian Knots

Student: Dunaykin Alexander

Supervisor: Sergei Lando

Faculty: Faculty of Mathematics

Educational Programme: Mathematics (Master)

Final Grade: 8

Year of Graduation: 2018

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.

Full text (added May 31, 2018)

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