|Z_{Kup}|=|Z_{Henn}|^2 for Lens spaces

Details |Z_{Kup}|=|Z_{Henn}|^2 for Lens spaces |Z_{Kup}|=|Z_{Henn}|^2 for Lens spaces

2011-06-16

arxiv.org/abs/1106.3313v2

Mathematics

Quantum Algebra

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Scientific paper

M.\ Hennings and G.\ Kuperberg defined quantum invariants Z_{Henn} and Z_{Kup} of 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. Recently a fermionic generalization of the Turaev-Viro state sum TQFTs is proposed using Grassmann variables. We conjecture that the Kuperberg invariants for non-semisimple Hopf algebras are the partition functions of such "TQFTs for systems with fermions".

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