 
Summary: Documenta Math. 795
Divisibility of the Dirac Magnetic Monopole
as a TwoVector Bundle over the ThreeSphere
Christian Ausoni, Bjørn Ian Dundas and John Rognes
Received: September 10, 2008
Revised: October 18, 2008
Communicated by Lars Hesselholt
Abstract. We show that when the gerbe µ representing a magnetic
monopole is viewed as a virtual 2vector bundle, then it decomposes,
modulo torsion, as two times a virtual 2vector bundle . We therefore
interpret as representing half a magnetic monopole, or a semipole.
2000 Mathematics Subject Classification: 19D50, 55P43, 81S10, 81T40.
Keywords and Phrases: magnetic monopole, gerbe, twovector bundle,
higher algebraic Ktheory, topological Hochschild homology.
§1. Introduction
Let A be a connective Salgebra, where S is the sphere spectrum, and let
K(A) = K0(0(A)) × BGL(A)+
be its algebraic Ktheory space. The nat
ural map w: BGL1(A) K(A) is given by the inclusion of 1 × 1 matrices
BGL1(A) BGL(A), followed by the canonical map into the plus con
