2025/08/14 by Chae, John · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2508.10279
We introduce a three variable series invariant FK (y,z,q) for plumbed knot complements associated with a Lie superalgebra sl(2|1). The invariant is a generalization of the sl(2|1)-series invariant Z(q) for closed 3-manifolds introduced by Ferrari and Putrov and an extension of the two variable series invariant defined by Gukov and Manolescu (GM) to the Lie superalgebra. We derive a surgery formula relating FK (y,z,q) to Z(q) invariant. We find appropriate expansion chambers for certain infinite families of torus knots and compute explicit examples. Furthermore, we provide evidence for a non semisimple Spinc decorated TQFT from the three variable series. We observe that the super FK (y,z,q) itself and its results exhibit distinctive features compared to the GM series.