The boundary of an affine invariant submanifold
Dynamical Systems
2020-07-15 v4 Geometric Topology
Abstract
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.
Keywords
Cite
@article{arxiv.1508.01446,
title = {The boundary of an affine invariant submanifold},
author = {Maryam Mirzakhani and Alex Wright},
journal= {arXiv preprint arXiv:1508.01446},
year = {2020}
}
Comments
The only change in the newest version (post publication) is a minor correction to the one paragraph proof of Corollary 2.14 (3)