We construct the homotopy pullback of An-spaces and show some universal property of it. As the first application, we review Zabrodsky's result which states that for each prime p, there is a finite CW complex which admits an Ap-1-form but no Ap-form. As the second application, we investigate An-types of gauge groups. In particular, we give a new result on An-types of the gauge groups of principal SU(2)-bundles over S4, which is a complete classification when they are localized away from 2.
All Science Journal Classification (ASJC) codes
- Geometry and Topology