Narrow Results

The caloron correspondence can be understood as an equivalence of categories between G-bundles over circle bundles and LG ⋊_ρ S¹-bundles where LG is the group of smooth loops in G. We use it, and lifting bundle gerbes, to derive an explicit differential form based formula for the (real) string class of an LG ⋊_ρ S¹-bundle.

Studying the M-branes leads us naturally to new structures that we call Membrane-, Membrane^c, String^K(ℤ,3) and Fivebrane^K(ℤ,4) structures, which we show can also have twisted counterparts. We study some of their basic properties, highlight analogies with structures associated with lower levels of the Whitehead tower of the orthogonal group, and demonstrate the relations to M-branes.