A virtual link is said to be almost classical (AC) if it has a homologically trivial representative in some thickened surface Σ x [0,1], where Σ is a closed orientable surface. Since AC links bound Seifert surfaces, they provide a useful window for observing the geometric topology of virtual knots. Here we take a different approach and look at AC links through the lens of quantum topology. Two adjustments are needed to the existing theory. First, it is necessary to generalize the definition of AC to include virtual tangles and, in particular, virtual braids. Secondly, to distinguish AC and non-AC tangles, the additional structure of quantum supergroups is required.

The authors would like to express their thanks to K. Davis, C. Frohman, P. Pongtanapaisan, and R. Todd for numerous helpful conversations. The first named author was partially supported by funds and release time by The Ohio State University at Marion.