A New Proof of ${\mathbf{Z}}_{\mathbf{Kup}}=|{\mathbf{Z}}_{\mathbf{Henn}}{|}^2$ for Semisimple Hopf Algebras

Liang Chang

Hennings and Kuperberg defined quantum invariants $Z_{Henn}$ and $Z_{Kup}$ for closed oriented $3$-manifolds based on certain Hopf algebras, respectively. When the Hopf algebras ar…