Divisibility of the Dirac magnetic monopole as a two-vector bundle over the three-sphere

Abstract

We show that when the gerbe $\mu$ representing a magnetic monopole is viewed as a virtual 2-vector bundle, then it decomposes, modulo torsion, as two times a virtual 2-vector bundle $\varsigma$. We therefore interpret $\varsigma$ as representing half a magnetic monopole, or a semipole.