I saw that a cell-decomposition of a genus g non-orientable surface is $D^0\cup D^1\cup ...\cup D^g$. Can anyone explain why this is true?
Cell decomposition of non-orientable surfaces
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general-topology
non-orientable-surfaces
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1I think you are confusing two things. The simplest cell-decomposition for a genus 1 nonorientable surface has three cells, a $0$-cell, a $1$-cell and a $2$cell, which doesn't match your count. What you have written looks instead like a cell decomposition for $\mathbb{RP}^g$, or projective $g$-space. (The $g$-dimensional projective plane.) – 2011-12-07
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0Oh yeah. That's why it didn't make sense to me. Thanks – 2011-12-07