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- W4288286677 abstract "A finite abstract simplicial complex G defines a matrix L, where L(x,y)=1 if two simplicies x,y in G intersect and where L(x,y)=0 if they don't. This matrix is always unimodular so that the inverse g of L has integer entries g(x,y). In analogy to Laplacians on Euclidean spaces, these Green function entries define a potential energy between two simplices x,y. We prove that the total energy summing all matrix elements g(x,y) is equal to the Euler characteristic X(G) of G and that the number of positive minus the number of negative eigenvalues of L is equal to X(G)." @default.
- W4288286677 created "2022-07-28" @default.
- W4288286677 creator A5082554988 @default.
- W4288286677 date "2019-07-07" @default.
- W4288286677 modified "2023-09-25" @default.
- W4288286677 title "The energy of a simplicial complex" @default.
- W4288286677 doi "https://doi.org/10.48550/arxiv.1907.03369" @default.
- W4288286677 hasPublicationYear "2019" @default.
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