English

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 GL(11)GL(1|1)-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

R2 v1 2026-06-25T01:45:17.743Z