We classify all closed non-orientable P²-irreducible 3-manifolds with complexity up to 7, fixing two mistakes in our previous complexity-up-to-6 classification. We show that there is no such manifold with complexity less than 6, five with complexity 6 (the four flat ones and the filled Gieseking manifold, which is of type Sol), and three with complexity 7 (one manifold of type Sol, and the two manifolds of type H²xR with smallest base orbifolds).
Amendola, G., Martelli, B. (2005). Non-orientable 3-manifolds of complexity up to 7. TOPOLOGY AND ITS APPLICATIONS, 150(1-3), 179-195 [10.1016/j.topol.2004.11.011].
Non-orientable 3-manifolds of complexity up to 7
AMENDOLA, GENNARO;
2005
Abstract
We classify all closed non-orientable P²-irreducible 3-manifolds with complexity up to 7, fixing two mistakes in our previous complexity-up-to-6 classification. We show that there is no such manifold with complexity less than 6, five with complexity 6 (the four flat ones and the filled Gieseking manifold, which is of type Sol), and three with complexity 7 (one manifold of type Sol, and the two manifolds of type H²xR with smallest base orbifolds).
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