Return to Question

Consider a 3-manifold $M$ with a boundary, which is a genus $g\geq 1$ surface $\Sigma$. Fix a triangulation $T$ of $\Sigma.$ Then Turaev-Viro invariants $TV_q(M)$ are functions, assigning to integer labelings of the edges of $T$ certain $q-$polynomials.

For a closed $3-$manifolds $q$ needs to be a root of unity for the invariant to be defined, but I think that for a general 3-manifold with boundary TV(M) could be constructed as a q-difference module by convolving 6j-symbols.

Question: is function $TV_n(M)$ known (expected) to be $q-$holonomic?

Consider a 3-manifold $M$ with a boundary, which is a genus $g\geq 1$ surface $\Sigma$. Fix a triangulation $T$ of $\Sigma$. Then Turaev-Viro invariants $TV_q(M)$ are functions, assigning to integer labelings of the edges of $T$ certain $q$-polynomials.

For a closed $3$-manifolds $q$ needs to be a root of unity for the invariant to be defined, but I think that for a general 3-manifold with boundary TV(M) could be constructed as a $q$-difference module by convolving 6j-symbols.

Question: is function $TV_n(M)$ known (expected) to be $q$-holonomic?

Consider a 3-manifold $M$ with a boundary, which is a genus $g\geq 1$ surface $\Sigma$. Fix a triangulation $T$ of $\Sigma.$ Then Turaev-Viro invariants $TV_q(M)$ are functions, assigning to integer labelings of the edges of $T$ certain $q-$polynomials.

For a closed $3-$manifolds $q$ needs to be a root of unity for the invariant to be defined, but I think that for a manifold with boundary it can be viewed as a formal variable.

Question: is function $TV_n(M)$ known (expected) to be $q-$holonomic?

Consider a 3-manifold $M$ with a boundary, which is a genus $g\geq 1$ surface $\Sigma$. Fix a triangulation $T$ of $\Sigma.$ Then Turaev-Viro invariants $TV_q(M)$ are functions, assigning to integer labelings of the edges of $T$ certain $q-$polynomials.

For a closed $3-$manifolds $q$ needs to be a root of unity for the invariant to be defined, but I think that for a general 3-manifold with boundary TV(M) could be constructed as a q-difference module by convolving 6j-symbols.

Question: is function $TV_n(M)$ known (expected) to be $q-$holonomic?