Lecture . Generalized Euler Characteristics and K-theory
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چکیده
is number ostensibly depends upon the chosen cell decomposition, but one of the first stories we learn about homology is that, in fact, it’s an invariant of the space itself ! To remind ourselves why, let’s consider an algebraic Euler characteristic. .. Definition. Suppose E = (E∗, ∂) a bounded complex of finite dimensional rational vector spaces. e Euler characteristic of C is the alternating sum of the dimensions of the vector spaces therein: χ(E) = ∑
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