English

Teichm\"uller theory and collapse of flat manifolds

Differential Geometry 2019-02-21 v1 Metric Geometry

Abstract

We provide an algebraic description of the Teichm\"uller space and moduli space of flat metrics on a closed manifold or orbifold and study its boundary, which consists of (isometry classes of) flat orbifolds to which the original object may collapse. It is also shown that every closed flat orbifold can be obtained by collapsing closed flat manifolds, and the collapsed limits of closed flat 3-manifolds are classified.

Keywords

Cite

@article{arxiv.1705.08431,
  title  = {Teichm\"uller theory and collapse of flat manifolds},
  author = {Renato G. Bettiol and Andrzej Derdzinski and Paolo Piccione},
  journal= {arXiv preprint arXiv:1705.08431},
  year   = {2019}
}

Comments

LaTeX2e, 25 pages, 17 figures