### Abstract

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.

Original language | English |
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Pages (from-to) | 826-832 |

Number of pages | 7 |

Journal | Journal of Pure and Applied Algebra |

Volume | 216 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 1 2012 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory