On Kirchhoff's theorems with coefficients in a line bundle
Algebraic Topology
2013-06-11 v2 Combinatorics
Abstract
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 flat unitary line bundle.
Keywords
Cite
@article{arxiv.1207.2822,
title = {On Kirchhoff's theorems with coefficients in a line bundle},
author = {Michael J. Catanzaro and Vladimir Y. Chernyak and John R. Klein},
journal= {arXiv preprint arXiv:1207.2822},
year = {2013}
}
Comments
Added improvements to the proof of Theorem C. Added some additional figures