## A gravitational effective action on a finite triangulation as a discrete model of continuous concepts

##
*Albert Ko and Martin Rocek*

**Address.**

M. Rocek, C. N. Yang Institute for Theoretical Physics, SUNY, Stony Brook, NY 11794-3840, USA

Institute for Theoretical Physics, University of Amsterdam, 1018 XE Amsterdam, The Netherlands

A. Ko, Ward Melville High School

**E-mail. **

rocek@insti.physics.sunysb.edu

**Abstract.**

We recall how the Gauss-Bonnet theorem can be interpreted as a finite
dimensional index theorem. We describe the construction given in
{\tt 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.