# Projections and hulls in the curve graph

Robert Tang
University of Warwick
27 February 2013, 3pm - 4pm, AGR or Carslaw 451, University of Sydney

## Abstract

The curve graph $$C(S)$$ associated to a surface $$S$$ is a graph whose vertices are simple closed curves on $$S$$ and whose edges are spanned by pairs of disjoint curves. This provides a combinatorial means for understanding the coarse geometry of mapping class groups, Teichmueller space and hyperbolic 3-manifolds. After presenting some basic definitions, I will describe a coarse analogue of a "convex hull" for a finite set of vertices in $$C(S)$$ using only intersection number information. I then show how these results can be used to give a combinatorial approximation for nearest point projection maps to subgraphs of the curve graph which arise naturally from surface covering maps.