Flat GL(1|1)-connections and fatgraphs

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 gra...

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Bibliographic Details
Published in:Journal of geometry and physics 2023-09, Vol.191, p.104880, Article 104880
Main Authors: Bourque, Andrea, Zeitlin, Anton M.
Format: Article
Language:English
Subjects:
Character variety
Fatgraph
Moduli space
Super Lie groups
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Summary: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.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2023.104880