A study of time reversal symmetry of abelian anyons

Abstract

We perform a study of time reversal symmetry of abelian anyons A in 2+1 dimensions, in the spin structure independent cases. We will find the importance of the group C of time-reversal-symmetric anyons modulo anyons composed from an anyon and its time reversal. Possible choices of local Kramers degeneracy are given by quadratic refinements of the braiding phases of C, and the anomaly is then given by the Arf invariant of the chosen quadratic refinement. We also give a concrete study of the cases when |A| is odd or A=(ℤ2)N.