• Study the relation between (combinatorial) length of a free homotopy class of curves on a surface and its self-intersection

  • Characterization of simple closed curves in terms of the Goldman Turaev Lie bialgebra. More generally, counting minimal intersection and self intersection numbers by means of this Lie bialgebra.
     


Research

Interests:
Low dimensional topology, geometric topology, combinatorial group theory.
curves

  • Configurations    of curves on surfaces which have minimal intersection and  self-intersection.

  • A presentation of the Goldman-Turaev Lie bialgebra of curves on closed surfaces.