English

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

R2 v1 2026-06-21T21:34:19.399Z