2|1-dimensional variants of the K-theory (1|1) conjecture

Establish 2|1-dimensional analogs of the Stolz–Teichner K-theory triangular diagram—construct the corresponding quantization and cocycle maps and prove their commutativity—extending beyond the 1|1-dimensional case in which the theorem is known.

Background

The 1|1-dimensional version relating supersymmetric quantum mechanics and K-theory is essentially established, subject to technical caveats. However, arguments used there are believed not to generalize efficiently to 2|1 dimensions.

The authors explicitly state that variations on this K-theory conjecture remain open in the 2|1-dimensional setting, highlighting a gap in current techniques and suggesting direction via super-parallel transport for infinite rank (Remark 3.11).