ORIENTATIONS ON 2-VECTOR BUNDLES AND DETERMINANT GERBES
2013 (English)In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 113, no 1, 63-82 p.Article in journal (Refereed) Published
In a paper from 2009, a half magnetic monopole was discovered by Ausoni, Dundas, and Rognes. This describes an obstruction to the existence of a continuous map K (ku) -> B(ku*) with determinant like properties. This magnetic monopole is in fact an obstruction to the existence of a map from K (ku) to K (Z, 3), which is a retract of the natural map K (Z, 3) -> K (ku); and any sensible definition of determinant like should produce such a retract. In this paper we describe this obstruction precisely using monoidal categories. By a result from 2011 by Baas, Dundas, Richter and Rognes K (ku) classifies 2-vector bundles. We thus define the notion of oriented 2-vector bundles, which removes the obstruction by the magnetic monopole. We use this to define an oriented K-theory of 2-vector bundles with a lift of the natural map from K (Z, 3). It is then possible to define a retraction of this map and since K (Z, 3) classifies complex gerbes we call this a determinant gerbe map.
Place, publisher, year, edition, pages
2013. Vol. 113, no 1, 63-82 p.
IdentifiersURN: urn:nbn:se:uu:diva-210760ISI: 000325836900005OAI: oai:DiVA.org:uu-210760DiVA: diva2:664180