TL;DR
This paper revisits Gunningham's formula for spin Hurwitz numbers using a gluing theorem, providing a new proof and a formalism for the associated topological quantum field theory.
Contribution
It offers a re-proof of Gunningham's formula via the gluing theorem and introduces a natural TQFT formalism derived from it.
Findings
Re-proved Gunningham's formula using the gluing theorem
Described a TQFT formalism induced from the gluing theorem
Provided insights into the structure of spin Hurwitz numbers
Abstract
Gunningham [G] constructed an extended topological quantum field theory (TQFT) to obtain a closed formula for all spin Hurwitz numbers. In this note, we use the gluing theorem in [LP2] to re-prove the Gunningham's formula. We also describe a TQFT formalism naturally induced from the gluing theorem.
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