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.
@article{108031,
author = {Albert Ko and Martin Ro\v cek},
title = {A gravitational effective action on a finite triangulation as a discrete model of continuous concepts},
journal = {Archivum Mathematicum},
volume = {042},
year = {2006},
pages = {245-251},
zbl = {1164.83300},
mrnumber = {2322411},
language = {en},
url = {http://dml.mathdoc.fr/item/108031}
}
Ko, Albert; Roček, Martin. A gravitational effective action on a finite triangulation as a discrete model of continuous concepts. Archivum Mathematicum, Tome 042 (2006) pp. 245-251. http://gdmltest.u-ga.fr/item/108031/
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