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How to interpret sections over the $\mathrm{SU}(2)$ character variety as sections over the $\mathrm{SL}(2,\mathbb{C})$ character variety?
The motivation for this question comes from the Volume Conjecture of Kashaev-Murakami-Murakami. The Jones family of invariants of knots and $3$-manifolds can all be defined using $\mathrm{SU}(2)$ and ...
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