Handle-cut formula for anyon ground-state degeneracy ($\dim V({\Sigma }_g)=[({\sum }_a{N}_a{N}_{\bar{a}}{)}^g{]}_{11}$)

Cutting one nonseparating circle on each handle of a closed orientable surface gives a sphere with $g$ pairs of oppositely oriented boundary circles. The topological quantum field theory gluing rule sums over the paired anyon labels $a,\bar{a}$. The resulting anyon fusion matrix formula becomes $\dim V({\Sigma }_g)={\mathcal{D}}^{2g-2}{\sum }_a{d}_a^{2-2g}$ by the Verlinde formula.