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A NOTE ON GUNNINGHAM’S FORMULA

Gunningham [‘Spin Hurwitz numbers and topological quantum field theory’, Geom. Topol. 20(4) (2016), 1859–1907] constructed an extended topological quantum field theory (TQFT) to obtain a closed formula for all spin Hurwitz numbers. In this note, we use a gluing theorem for spin Hurwitz numbers to re-prove Gunningham’s formula. We also describe a TQFT formalism naturally induced by the gluing theorem.