|Z_{Kup}|=|Z_{Henn}|^2 for Lens spaces
  M. Hennings and G. Kuperberg defined quantum invariants Z_{Henn} and Z_{Kup} of closed oriented 3-manifolds based on certain Hopf algebras, respectively. We prove that |Z_{Kup}|=|Z_{Henn}|^2 for lens spaces when both invariants are based on factorizable finite dimensional ribbon Hopf algebras. 
Liang Chang and Zhenghan Wang
math.QA math.GT