2 problems

Let $a$ be fixed, and suppose that $r$ is even and $a$ is odd. Let $W_g^\pm(a,r)$ denote the refinement of Witten's class according to spin parity, and let…

Let $(a_1,\ldots,a_n)$ be a partition of $2g-2$ with non-negative parts. For sufficiently large $r$, let $\mathcal{W}_{g; a_1, \dots, a_n}(r)=r^{g-1}W^r_{g,n}(a_1, \dots, a_n)$ be…