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Category: <span>simplicial complex</span>
Home Archive for category "simplicial complex"

Category: simplicial complex

More on Analytic Torsion
Graph theory, Riemannian Geometry, simplicial complex

More on Analytic Torsion

By oliverknill January 16, 2022 January 16, 2022  torsion

We report on some progress on analytic torsion A(G) for graphs. A(G) is a positive rational number attached to a network. We can compute it for contractible graphs or spheres.

Continue reading"More on Analytic Torsion"
More on Ringed Complexes
discrete geometry, simplicial complex

More on Ringed Complexes

By oliverknill October 19, 2020 October 19, 2020

The results mentioned in the slides before are now written down. This document contains a proof of the energy relation . There are several reason for setting things up more generally and there is also some mentioning in the article: allowing general rings and not just division algebras extends the …

Continue reading"More on Ringed Complexes"
Complex energized complexes
discrete geometry, Graph theory, physics, quantum calculus, simplicial complex

Complex energized complexes

By oliverknill August 17, 2020 August 23, 2020

The energy theorem for simplicial complexes equipped with a complex energy comes with some surpises.

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Energized Simplicial Complexes
discrete geometry, Graph theory, quantum calculus, simplicial complex

Energized Simplicial Complexes

By oliverknill August 19, 2019 August 23, 2019

If a set of set is equipped with an energy function, one can define integer matrices for which the determinant, the eigenvalue signs are known. For constant energy the matrix is conjugated to its inverse and defines two isospectral multi-graphs.

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The counting matrix of a simplicial complex
discrete geometry, Graph theory, quantum calculus, simplicial complex, zeta functions

The counting matrix of a simplicial complex

By oliverknill July 22, 2019 November 25, 2019

The counting matrix of a simplicial complex has determinant 1 and is isospectral to its inverse. The sum of the matrix entries of the inverse is the number of elements in the complex.

Continue reading"The counting matrix of a simplicial complex"
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