LAUSR

A bstractWe perform a study of time reversal symmetry of abelian anyons A$$ \mathcal{A} $$ in 2+1 dimensions, in the spin structure independent cases. We will find the importance of the group C$$ \mathcal{C} $$ 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$$ \mathcal{C} $$, 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$$ \mathcal{A} $$| is odd or A=ℤ2N$$ \mathcal{A}={\left({\mathrm{\mathbb{Z}}}_2\right)}^N $$.