2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154251We study the structure of the Kauffman algebra of a surface with parameter equal to sqrt(-1). We obtain an interpretation of this algebra as an algebra of parallel transport operators acting on sections of a line bundle over the moduli space of flat connections in a trivial SU(2)-bundle over the surface. We analyse the asymptotics of traces of curve-operators in TQFT in non standard regimes where the root of unity parametrizing the TQFT accumulates to a root of unity. We interpret the case of sqrt(-1) in terms of parallel transport operators.16 pages, 2 figuresGeometric TopologyQuantum Algebra57M27; 57M50; 57M56; 37E30text