After introducing virtual homotopy, I will discuss two methods of estimating the minimum number of self-intersection points of a curve in a given virtual homotopy class. The first uses the based matrix invariant of Turaev. The second uses an operation mu that generalizes Turaev's Lie cobracket for virtual curves. We compare these estimates and construct a family of examples such that the second estimate is sharp.
Geometry-Topology Seminar
Thursday, February 7, 2013 - 4:30pm
Patricia Cahn
University of Pennsylvania