Kuperberg invariants for balanced sutured 3-manifolds

Daniel López Neumann

doi:10.4153/s0008414x20000656

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arXiv · 1904.05786

Kuperberg invariants for balanced sutured 3-manifolds

Daniel López Neumann

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Abstract

We construct quantum invariants of balanced sutured 3-manifolds with a $Spin^{c}$ structure out of an involutive (possibly non-unimodular) Hopf superalgebra $H$. If $H$ is the Borel subalgebra of $U_{q}(\mathfrak{gl}(1|1))$, we show that our invariant is computed via Fox calculus and it is a normalization of Reidemeister torsion. The invariant is defined via a modification of a construction of G. Kuperberg, where we use the $Spin^{c}$ structure to take care of the non-unimodularity of $H$ or $H^{*}$.

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Daniel López Neumann. 2019-04-11. Kuperberg invariants for balanced sutured 3-manifolds. https://doi.org/10.4153/s0008414x20000656

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