The Euler Characteristic
نویسنده
چکیده
I will describe a few basic properties of the Euler characteristic and then I use them to prove special case of a cute formula due to Bernstein-Khovanskii-Koushnirenko. 1. Basic properties of the Euler characteristic The Euler characteristic is a function χ which associates to each reasonable topological space X an integer χ(X). For us a reasonable space would be a space which admits a finite simplicial decomposition (a.k.a. triangulation.) For example, all algebraic varieties are reasonable. In the sequel we will tacitly assume that all spaces are reasonable and so we will drop this attribute from our discourse. More explicitly, the Euler characteristic of X is defined as the alternating sum
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