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

### Summary

Summary: 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.

### Mathematics Subject Classification

19D50, 55P43, 81S10, 81T40

### Keywords/Phrases

magnetic monopole, gerbe, two-vector bundle, higher algebraic $K$-theory, topological Hochschild homology