Kirchhoff's theorems in higher dimensions and Reidemeister torsion
  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. 
Michael J. Catanzaro, Vladimir Y. Chernyak, John R. Klein
math.AT