Talk:Genus (mathematics)

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[edit] Open Annulus has genus 0

If you can include boundary points in the closed curve, you can cut the Annulus...

[edit] A pretzel has genus 2, and so has the number 8 and the letter B.

Shouldn't a pretzel be genus 3? Most pretzels I've seen have two big semicircular holes and one smaller triangular one.

pretzel!!! MotherFunctor 04:32, 15 May 2006 (UTC)

[edit] It is all wrong

The page is all wrong, I always thoght that genus is an invariant for surfaces only and nuber of holes is not metter, S^2, D^2, and cilinder all have geus zero. I thought to change it, but it seems that there is no standard agreement on when genus is defined, for sure oriented surfeces are included, it is used sometimes for nonorented, but with not oreinted it seems there is no standard def... Look at [1] and [2]

Tosha 23:49, 28 May 2004 (UTC)

I agree, see below. MotherFunctor 04:31, 15 May 2006 (UTC)

[edit] genus of the Bottle of Klein

The Bottle of Klein is a non-orientable surface of genus 1, not 2 as stated on this page. It is correct on [3].

(Citing a wiki page as reference is very weak, as is no signature!) Mathworld gives genus as the maximum number of non-intersecting Jordan curves such that their complement in the surface is path connected. This substantiates the above section "it's all wrong" and substantiates Klein's bottle is genus 2. MotherFunctor 04:30, 15 May 2006 (UTC)
Write K for the Klein bottle and P for the real projective plane. It can easily be shown that K = P # P, thus the (non-orientable) genus of K is 2. Morana (talk) 21:23, 7 April 2008 (UTC)