Topology Seminar: Eriko Hironaka

The deformation space of a rational map is a submanifold of Teichmueller space parameterizing maps that are combinatorially and dynamically equivalent. S. Koch and I recently showed that this space need not be connected, and can have infinitely many components. In this talk we describe some tools from algebraic geometry, and the topology of coverings that reveal the obstructions to connectedness, and give some evidence that connectedness may be achieved by passing to augmented Teichmueller space.