### 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 |
---|---|

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 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

**A note on homotopy types of connected components of Map(S ^{4}, BSU(2)).** / Tsutaya, Mitsunobu.

Research output: Contribution to journal › Article

^{4}, BSU(2))',

*Journal of Pure and Applied Algebra*, vol. 216, no. 4, pp. 826-832. https://doi.org/10.1016/j.jpaa.2011.10.020

}

TY - JOUR

T1 - A note on homotopy types of connected components of Map(S 4, BSU(2))

AU - Tsutaya, Mitsunobu

PY - 2012/4/1

Y1 - 2012/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84855229624&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855229624&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2011.10.020

DO - 10.1016/j.jpaa.2011.10.020

M3 - Article

AN - SCOPUS:84855229624

VL - 216

SP - 826

EP - 832

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 4

ER -