The covering type of closed surfaces and minimal triangulations
Geometric Topology
2017-12-11 v1 Algebraic Topology
Abstract
The notion of covering type was recently introduced by Karoubi and Weibel to measure the complexity of a topological space by means of good coverings. When X has the homotopy type of a finite CW-complex, its covering type coincides with the minimum possible number of vertices of a simplicial complex homotopy equivalent to X. In this article we compute the covering type of all closed surfaces. Our results completely settle a problem posed by Karoubi and Weibel, and shed more light on the relationship between the topology of surfaces and the number of vertices of minimal triangulations from a homotopy point of view.
Keywords
Cite
@article{arxiv.1712.02833,
title = {The covering type of closed surfaces and minimal triangulations},
author = {Eugenio Borghini and Elias Gabriel Minian},
journal= {arXiv preprint arXiv:1712.02833},
year = {2017}
}
Comments
6 pages