# Green functions of Energized complexes

@article{Knill2020GreenFO, title={Green functions of Energized complexes}, author={Oliver Knill}, journal={ArXiv}, year={2020}, volume={abs/2010.09152} }

If h is a ring-valued function on a simplicial complex G we can define two matrices L and g, where the matrix entries are the h energy of homoclinic intersections. We know that the sum over all h values on G is equal to the sum of the Green matrix entries g(x,y). We also have already seen that that the determinants of L or g are both the product of the h(x). In the case where h(x) is the parity of dimension, the sum of the energy values was the standard Euler characteristic and the determinant…

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