Gottlieb has shown that connected components of Map(S 4, BSU(2)) are the classifying spaces of gauge groups of principal SU(2)-bundles over S 4. Tsukuda has investigated the homotopy types of connected components of Map(S 4, BSU(2)). But unfortunately, his proof is not complete for p=2. In this paper, we give a complete proof. Moreover, we investigate the further divisibility of ε i defined in Tsukuda's paper. We apply this to classification problem of gauge groups as A n-spaces.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory