Untwisted algebraic 1-torsion in the Corollary 8.4 examples

Let $Y$ be the unit cotangent bundle of a hyperbolic surface, and let $(M=\Sigma\times Y,\xi_k)$ be the corresponding $5$-dimensional contact manifold of Theorem 5d. These examples are understood for $k\geq 3$ in Corollary 8.4, while the conjecture asserts the property for any $k\geq 1$. Untwisted algebraic 1-torsion conjecture. The examples of Corollary 8.4 have untwisted algebraic $1$-torsion for any $k\geq 1$. For $k\geq 3$, this would produce an infinite family of $5$-dimensional contact manifolds with no Giroux torsion and algebraic $1$-torsion. The conjecture is motivated by geometric evidence and by the relationship between symplectic field theory and string topology; it remains open.