Kuperberg invariants for balanced sutured 3-manifolds

Abstract

We construct quantum invariants of balanced sutured 3-manifolds with a $Spi{n}^c$ 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 $Spi{n}^c$ structure to take care of the non-unimodularity of $H$ or $H^{\ast }$.

41 pages. Several changes: all Hopf algebra expressions are now written in tensor network notation, previous Sect. 3 is now part of Sect. 2, previous Subsections 5.1, 5.2 are now part of Sect. 3, arguments of Sect. 6 (previous Sect. 7) have been streamlined. To be published in Canadian Journal of Mathematics

References in corpus (2)

• On the relation between the WRT invariant and the Hennings invariant
• On Two Invariants of Three Manifolds from Hopf Algebras

Cited by in corpus (1)

• 4-Manifold Invariants From Hopf Algebras