A note on Gunningham's formula

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.Comment: Typos fixed and exposition change

Local GW Invariants of Elliptic Multiple Fibers

We use simple geometric arguments to calculate the dimension zero local Gromov-Witten invariants of elliptic multiple fibers. This completes the calculation of all dimension zero GW invariants of elliptic surfaces with $p_g>0$.Comment: To appear in Pure Appl. Math.

Degree three spin Hurwitz numbers

Recently, Gunningham \cite{G} calculated all spin Hurwitz numbers in terms of combinatorics of Sergeev algebra. In this paper, we use a spin curve degeneration to obtain a recursion formula for degree three spin Hurwitz numbers.Comment: typos fixed, references added, motivation and comment on higher degree cases adde