📝 SummarXiv

Abstract

In $(2+1)$-dimensional topological quantum field theories (TQFTs), the action of a global symmetry group on the anyon system is one of the central topics of research. Owing to the subtle categorical nature of anyons, such group actions do not automatically satisfy associativity. The obstruction is captured by a cohomology class, known as the $H^3$ obstruction, whose presence signals a failure of group associativity. In these cases, the symmetry structure is no longer described by an ordinary group, but instead by a $2$-group -- a group-like structure extended by a $1$-form symmetry. In this short note, we prove that the $H^3$ obstruction for time-reversal symmetry always vanishes in abelian bosonic TQFTs.