Super-representations of 3-manifolds and torsion polynomials

Abstract: Torsion polynomials connect the genus of a hyperbolic knot (a topological invariant) with the discrete faithful representation (a geometric invariant). Using a new combinatorial structure of an ideal triangulation of a 3-manifold that involves edges as well as faces, we associate a polynomial to a cusped hyperbolic manifold that conjecturally agrees with the

B C^{2}

-torsion polynomial, which conjecturally detects the genus of the knot. The new combinatorics is motivated by super-geometry in dimension 3, and more precisely by super-Ptolemy assignments of ideally triangulated 3-manifolds and their

m a t h r m {O S p}_{2 | 1} (B C)

-representations. Extended section 4, and added superalgebras with a single odd generator.

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