1206.1986 (Adam Sawicki)

Discrete Morse functions for graph configuration spaces    [PDF]

Adam Sawicki

We present a new formulation of discrete Morse theory for two-particle graph configuration spaces. In contrast to previous constructions, which are based on discrete Morse vector fields, our approach is through Morse functions, which have a nice physical interpretation as two-body potentials constructed from one-body potentials. We also give a brief introduction to discrete Morse theory. Our motivation comes from the problem of quantum statistics for particles on networks, for which generalised versions of anyon statistics can appear.

View original: http://arxiv.org/abs/1206.1986