Geodesic
A gravitational effective action on a finite triangulation as a discrete model of continuous concepts
Archivum mathematicum, Tome 42 (2006) no. 5, pp. 245-251.

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We recall how the Gauss-Bonnet theorem can be interpreted as a finite dimensional index theorem. We describe the construction given in hep-th/0512293 of a function that can be interpreted as a gravitational effective action on a triangulation. The variation of this function under local rescalings of the edge lengths sharing a vertex is the Euler density, and we use it to illustrate how continuous concepts can have natural discrete analogs.
Classification : 83C27, 83C80 
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Ko, Albert; Roček, Martin. A gravitational effective action on a finite triangulation as a discrete model of continuous concepts. Archivum mathematicum, Tome 42 (2006) no. 5, pp. 245-251. http://geodesic.mathdoc.fr/item/ARM_2006__42_5_a11/