A finite abstraact simplicial complex or a finite simple graph comes with a natural finite topological space. Some quantities like the Euler characteristic or the higher Wu characteristics are all topological invariants. One can also reformulate the Lefschetz fixed point theorem for continuous maps on finite topological spaces.
The Wu characteristic of a simplicial complex is the eigenvalue of an
eigenvector to a matrix L J, where L is the connection Laplacian and J
a checkerboard matrix. The eigenvector has components whicih are
Wu intersection numbers.
[Update, March 20, 2018: see the ArXiv text. See also an update blog entry with some Mathematica code. More mathematica code can be obtained from the TeX Source of the ArXiv article.]. Classical calculus we teach in single and multi variable calculus courses has an elegant analogue on finite simple …
