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May 6, 2011 at 7:45 vote accept Tony Huynh
May 6, 2011 at 4:03 answer added Bill Thurston timeline score: 10
May 6, 2011 at 1:26 answer added Qiaochu Yuan timeline score: 9
May 5, 2011 at 23:43 answer added Gerry Myerson timeline score: 2
May 5, 2011 at 23:04 comment added Sergey Melikhov Tony, I wouldn't care if your question was not about terminology. Reading it literally, "It is well-known that up to homeomorphism, ..., where $N_k$ is the sphere with $k$ crosscaps." I did get an impression that a crosscap is referred to as a $2$-manifold. If that is a standard terminology somewhere, fine. I was not used to it.
May 5, 2011 at 22:19 comment added Tony Huynh @Sergey: I don't think I ever said a crosscap is a surface. Correctly me if I'm wrong, but I thought that the term sphere with $k$ crosscaps was pretty widely used to mean the surface obtained by cutting $k$ holes out a sphere and gluing a Moebius band along the boundary of each hole?
May 5, 2011 at 22:09 comment added Simon Rose @Tony - The problem with calling this "generalized genus" is that a generalization of a quantity should agree with the original one where they are both defined. However, in this case your generalized genus of a torus is 2, while the genus is 1. This seems not to be ideal.
May 5, 2011 at 21:38 comment added Sergey Melikhov A crosscap is not a surface but a singularity of a generic map of the surface into $\Bbb R^3$. The surface is called the Moebius band.
May 5, 2011 at 21:21 history edited Tony Huynh CC BY-SA 3.0
added reference tag
May 5, 2011 at 21:16 comment added Tony Huynh I am just wondering how badly I would be bastardizing nomenclature if I just called it genus?
May 5, 2011 at 21:14 comment added Tony Huynh Thanks. Yes, I thought of using that, but I didn't really want to bring in homology, and I thought there would be a standard name like say generalized genus to use.
May 5, 2011 at 21:09 comment added Qiaochu Yuan Isn't this just $\dim H_1$ (say with rational coefficients)?
May 5, 2011 at 20:57 answer added Simon Rose timeline score: 5
May 5, 2011 at 20:46 history asked Tony Huynh CC BY-SA 3.0