# Euler characteristic and subdivisions

Given a finite CW complex $X$ we define its Euler characteristic to be $\sum(-1)^k c_k$ where $c_k$ is the number of $k$-cells of $X$. It is not hard to show that the Euler characteristic of a CW complex $X$ is independent of the CW structure given to $X$.But what about the following question: Suppose $X$ and $Y$ are finite CW-complexes of the same dimension such that they have the same Euler characteristic. Are there subdivisions of $X$ and $Y$ such that the number of $k$-cells of $X$ under its new subdivision equals the number of $k$-cells of $Y$ under its new subdivision?

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