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Non-orientable 3-manifolds Ask Question. Asked 1 year, 2 months ago. Active 1 year ago. Viewed times.

Finite groups and flows on 2-manifolds

At the same time I have the following additional questions about non-orientable 3-manifolds. EDIT I add following new question. Marek Mitros. Marek Mitros Marek Mitros 1, 8 8 silver badges 29 29 bronze badges. What you see in dimension 2 is a very special case. B No again.

C The boundary of a regular neighbourhood, yes. The neighbourhood itself is the associated disc bundle to the Klein bottle.

On the Groups of Orientable Two-Manifolds

At least we can sort irreducible non-orientable 3-manifolds by genus of Stiefel-Whitney surface. So there are no non-trivial spheres. I guess this is called "solid Klein bottle". YCor YCor Can you explain me last sentence of your answer? How "torsion-free" lead to orientability? My understanding is that loop changing orientation is infinite order in fundamental group of 3-manifold.

Someone answered me on stack exchange, that there are no finite order elements in fundamental group of prime 3-manifold with infinte fundamental group.

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So it's indeed orientable. Sign up or log in Sign up using Google.

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Finite groups and flows on 2-manifolds — University of Illinois at Urbana-Champaign

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