Non-orientable 3-manifolds of small complexity

Details Non-orientable 3-manifolds of small complexity Non-orientable 3-manifolds of small complexity

2002-11-05

arxiv.org/abs/math/0211092v3

Topology Appl. 133 (2003), 157-178

Mathematics

Geometric Topology

27 pages, 12 figures. Two mistakes contained in the previous version are fixed: there is a Sol manifold with complexity 6, and

Scientific paper

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.

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