This is from an intro topology course. How can I go about finding an explicit embedding for the Klein bottle in this situation?
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Edit: my argument that there is no such embedding was wrong. My error was assuming that the $(S^1\times S^2,S^1\times S^2\setminus K)$ is what Hatcher calls a "good pair." See here https://math.stackexchange.com/questions/1202356/embedd-the-klein-bottle-into-a-3-manifold?rq=1 – pancini Nov 19 '19 at 23:51