Project IV 2015-2016

Curves on surfaces

Anna Felikson and Pavel Tumarkin


Curves on surfaces are elementary objects encoding a lot of topological and geometric properties of surfaces.
    How do the curves intersect? How many (different) closed curves can you place in a surface without intersection? Which groups of transformations are acting on the curves? How many lengths of the curves you need to know to recover a precise metric structure of the surface?
      Studying the curves from topological, combinatorial or geometrical point of view one can reach the following (simple, advanced or very advanced) areas: Anna Felikson will supervise in Michaelmas and Pavel Tumarkin in Epiphany.
      Prerequisites: Algebra II and either Topology III or Geometry III


      Many of the basic notions for the project are introduced in the course Some of the more advanced topics are described in the following books: Other topics are studied in numerous expository and research papers, you may start from ones listed here.

        email: Anna Felikson, Pavel Tumarkin