Talk:Crosscap number

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Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 00:55, 21 May 2007 (UTC)

How does the cross-cap fit in with this? I seem to recal the Euler characteristic is related to the number of cross-caps but the details escape me. --Salix alba (talk) 19:54, 24 September 2006 (UTC)

If you consider the classification of surfaces, for compact non-orientable surfaces, the classification states for a given Euler characteristic and specified number of boundary components, we have connected sum of a determined number of projective planes minus discs (to get the boundary components). "Cross-cap" can loosely refer to these summands. So the definition currently given is equivalent to counting the number of such crosscaps. --C S (Talk) 23:54, 9 March 2007 (UTC)