Flat $GL(1|1)$-connections and fatgraphs
Geometric Topology
2023-07-07 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Quantum Algebra
Representation Theory
Abstract
We study the moduli space of flat -connections on a punctured surface from the point of view of graph connections. To each fatgraph, a system of coordinates is assigned, which involves two bosonic and two fermionic variables per edge, subject to certain relations. In the case of trivalent graphs, we provide a closed explicit formula for the Whitehead moves. In addition, we discuss the invariant Poisson bracket.
Cite
@article{arxiv.2208.08033,
title = {Flat $GL(1|1)$-connections and fatgraphs},
author = {Andrea Bourque and Anton M. Zeitlin},
journal= {arXiv preprint arXiv:2208.08033},
year = {2023}
}
Comments
v2: 13 pages, minor revisions