Torus cannot collapse to a segment
Differential Geometry
2020-05-12 v2
Abstract
In earlier work, we analyzed the impossibility of codimension-one collapse for surfaces of negative Euler characteristic under the condition of a lower bound for the Gaussian curvature. Here we show that, under similar conditions, the torus cannot collapse to a segment. Unlike the torus, the Klein bottle can collapse to a segment; we show that in such a situation, the loops in a short basis for homology must stay a uniform distance apart.
Cite
@article{arxiv.2002.07523,
title = {Torus cannot collapse to a segment},
author = {Mikhail G. Katz},
journal= {arXiv preprint arXiv:2002.07523},
year = {2020}
}
Comments
8 pages, Journal of Geometry 111, Article number: 13 (2020)