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A gravitational effective action on a finite triangulation as a discrete model of continuous concepts. (English) Zbl 1164.83300
Summary: We recall how the Gauss-Bonnet theorem can be interpreted as a finite dimensional index theorem. We describe the construction given in A. Ko and M. Roček [A gravitational effective action on a finite triangulation JHEP 0603 (2006)] 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.
MSC:
83C27 Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory
83C80 Analogues of general relativity in lower dimensions
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