Non-orientable 3-manifolds of small complexity
Geometric Topology
2007-05-23 v3
Abstract
We classify all closed non-orientable P2-irreducible 3-manifolds having complexity up to 6 and we describe some having complexity 7. We show in particular that there is no such manifold with complexity less than 6, and that those having complexity 6 are precisely the 4 flat non-orientable ones and the filling of the Gieseking manifold, which is of type Sol. The manifolds having complexity 7 we describe are Seifert manifolds of type H2 x S1 and a manifold of type Sol.
Keywords
Cite
@article{arxiv.math/0211092,
title = {Non-orientable 3-manifolds of small complexity},
author = {Gennaro Amendola and Bruno Martelli},
journal= {arXiv preprint arXiv:math/0211092},
year = {2007}
}
Comments
27 pages, 12 figures. Two mistakes contained in the previous version are fixed: there is a Sol manifold with complexity 6, and the examples with complexty 7 are Sol and H2xS1 (see the abstract)