Kirchhoff's theorems in higher dimensions and Reidemeister torsion
Abstract
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 application, we give a formula expressing Reidemeister torsion as an enumeration of higher dimensional spanning trees.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2012
- DOI:
- 10.48550/arXiv.1206.6783
- arXiv:
- arXiv:1206.6783
- Bibcode:
- 2012arXiv1206.6783C
- Keywords:
-
- Mathematics - Algebraic Topology;
- 55J15;
- 57M15;
- 57Q10 (Primary) 05C05;
- 05C21;
- 05E45;
- 82C31 (Secondary)
- E-Print:
- Fixed several typos