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Aug 19, 2010 at 11:01 comment added JME Hi Dave, I just want to mention that your definition using excision actually also helps with the algebraic definition since the Euler characteristic you refer to matches the topological Euler characteristic and therefore can be defined purely algebraically using the Chern-MacPherson class. I discuss it in my answer.
Aug 19, 2010 at 1:01 history answered Dave Anderson CC BY-SA 2.5