Dimers and linear foam

Richard Kenyon (Brown)

Abstract :

We study certain natural configuration spaces of points and lines in R^2, as a model of "linear foam". We find global coordinates giving explicit homeomorphisms with R^n. The spaces of cell areas and cell boundary slopes are also shown to be topologically trivial.

These results show how the Kasteleyn matrix of dimer theory arises naturally as a differential. Applications in three dimensions will also be given.