Euler characteristic (original) (raw)

Next, if K is a finite CW complex, let αi be the number of i-cells in K. The Euler characteristic of Kis defined to be

If X is a finite polyhedron, with triangulation K, a simplicial complex, then the Euler characteristic of X is χ⁢(K). It can be shown that all triangulations of X have the same value for χ⁢(K) so that this is well-defined.

Finally, if C={Cq} is a finitely generated graded group, then the Euler characteristic of C is defined to be