## Abstract

We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of particles constrained to move in a topological space X. The framework involves a study of isomorphism classes of flat complex vector bundles over the configuration space of X which can be achieved by determining its homology groups. We apply this methodology for configuration spaces of graphs. As a conclusion, we provide families of graphs which are good candidates for studying simple effective models of anyon dynamics as well as models of non-abelian anyons on networks that are used in quantum computing. These conclusions are based on our solution of the so-called universal presentation problem for homology groups of graph configuration spaces for certain families of graphs.

Original language | English |
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Pages (from-to) | 921-973 |

Number of pages | 53 |

Journal | Communications in Mathematical Physics |

Volume | 371 |

Issue number | 3 |

Early online date | 9 Oct 2019 |

DOIs | |

Publication status | Published - 1 Nov 2019 |