CLASSIFICATION OF NODAL CURVES ON SURFACES AND BRAID INVARIANTS

This work is divided into two parts. The first part is devoted to the classification of nodal curves on closed surfaces under modified three Reidemeester moves obtained in the article "INCIDENCES AND TILING" by Sergey Fomin and Pavlo Pylyavsky, and finding the minimal element of these equivalence classes.
In the second part, several different braid invariants considered in the articles "Braids act on configurations of lines" and "Shear coordinates and braid invariants" by V.O. Manturov are calculated.