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math.AT2012★ 3 cited
Kirchhoff's theorems in higher dimensions and Reidemeister torsion
Michael J. Catanzaro, Vladimir Y. Chernyak, John R. Klein
Using ideas from algebraic topology and statistical mechanics, we generalize Kirchhoff's network and matrix-tree theorems to finite CW complexes of arbitrary dimension. As an appli…
math.AT2012
On Kirchhoff's theorems with coefficients in a line bundle
Michael J. Catanzaro, Vladimir Y. Chernyak, John R. Klein
We prove `twisted' versions of Kirchhoff's network theorem and Kirchhoff's matrix-tree theorem on connected finite graphs. Twisting here refers to chains with coefficients in a fla…