Kirchhoff's theorems in higher dimensions and Reidemeister torsion
Michael J. Catanzaro, Vladimir Y. Chernyak, John R. Klein
TL;DR
This paper extends Kirchhoff's theorems to higher-dimensional CW complexes using algebraic topology, providing a new formula linking Reidemeister torsion to higher-dimensional spanning trees.
Contribution
It introduces a generalization of Kirchhoff's theorems to arbitrary dimensions and relates Reidemeister torsion to higher-dimensional spanning trees.
Findings
Generalized Kirchhoff's theorems to CW complexes of any dimension
Derived a formula connecting Reidemeister torsion with higher-dimensional spanning trees
Utilized algebraic topology and statistical mechanics concepts
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsTopological and Geometric Data Analysis · Theoretical and Computational Physics · Complex Network Analysis Techniques