Arithmetic Geometry

Given a family $g: X \rightarrow S$ of smooth projective algebraic varieties over a number field $K$, one often wants to constrain the points $s$ in $S$ where the fibre $X_s$ acquires "extra" algebraic structure. A basic sort of constraint which is...

We use Teichmüller theory to construct a new geometric model for the classifying space of the mapping class group of a three-dimensional handlebody. Two consequences are obtained: (i) Chan-Galatius-Payne have shown that the homology of Kontsevich's...