Euler-Poincaré Characteristic on Homotopy-Equivalent Simplicial Complexes

Theorem

Let $K$ and $L$ be simplicial complexes.

Let $K$ and $L$ be homotopy-equivalent.

Then:

$\map \chi K = \map \chi L$

where $\map \chi K$ denotes the Euler-Poincaré characteristic of $K$.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Euler-Poincaré characteristic
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Euler-Poincaré characteristic