2015/08/06 by Maryam Mirzakhani, Mirzakhani, Maryam, Alex Wright +1 · 2 citations
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #math.DS #math.GT
paper · pdf · doi:10.48550/arxiv.1508.01446
The only change in the newest version (post publication) is a minor correction to the one paragraph proof of Corollary 2.14 (3)
arxiv created 2020/07/14 · arxiv updated 2020/07/15
We study the boundary of an affine invariant submanifold of a stratum of translation surfaces in a partial compactification consisting of all finite area Abelian differentials over nodal Riemann surfaces, modulo zero area components. The main result is a formula for the tangent space to the boundary. We also prove finiteness results concerning cylinders, a partial converse to the Cylinder Deformation Theorem, and a result generalizing part of the Veech dichotomy.