Flat $GL(1|1)$-connections and fatgraphs (2208.08033v2)

Published 17 Aug 2022 in math.GT, hep-th, math-ph, math.MP, math.QA, and math.RT

Abstract: We study the moduli space of flat $GL(1|1)$-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.

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