### Abstract

Let G be a compact connected Lie group and let P be a principal G-bundle over K. The gauge group of P is the topological group of automorphisms of P. For fixed G and K, consider all principal G-bundles P over K. It is proved in Crabb and Sutherland [Proc. London Math. Soc. (3) 81 (2000) 747-768] and Tsutaya [J. London Math. Society 85 (2012) 142-164] that the number of A_{n}-types of the gauge groups of P is finite if n < ∞ and K is a finite complex. We show that the number of A_{∞}-types of the gauge groups of P is infinite if K is a sphere and there are infinitely many P.

Original language | English |
---|---|

Article number | jtv025 |

Pages (from-to) | 181-191 |

Number of pages | 11 |

Journal | Journal of Topology |

Volume | 9 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 29 2015 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Geometry and Topology

### Cite this

_{∞}-types of gauge groups.

*Journal of Topology*,

*9*(1), 181-191. [jtv025]. https://doi.org/10.1112/jtopol/jtv025

**Infiniteness of A _{∞}-types of gauge groups.** / Kishimoto, Daisuke; Tsutaya, Mitsunobu.

Research output: Contribution to journal › Article

_{∞}-types of gauge groups',

*Journal of Topology*, vol. 9, no. 1, jtv025, pp. 181-191. https://doi.org/10.1112/jtopol/jtv025

_{∞}-types of gauge groups. Journal of Topology. 2015 Jul 29;9(1):181-191. jtv025. https://doi.org/10.1112/jtopol/jtv025

}

TY - JOUR

T1 - Infiniteness of A∞-types of gauge groups

AU - Kishimoto, Daisuke

AU - Tsutaya, Mitsunobu

PY - 2015/7/29

Y1 - 2015/7/29

N2 - Let G be a compact connected Lie group and let P be a principal G-bundle over K. The gauge group of P is the topological group of automorphisms of P. For fixed G and K, consider all principal G-bundles P over K. It is proved in Crabb and Sutherland [Proc. London Math. Soc. (3) 81 (2000) 747-768] and Tsutaya [J. London Math. Society 85 (2012) 142-164] that the number of An-types of the gauge groups of P is finite if n < ∞ and K is a finite complex. We show that the number of A∞-types of the gauge groups of P is infinite if K is a sphere and there are infinitely many P.

AB - Let G be a compact connected Lie group and let P be a principal G-bundle over K. The gauge group of P is the topological group of automorphisms of P. For fixed G and K, consider all principal G-bundles P over K. It is proved in Crabb and Sutherland [Proc. London Math. Soc. (3) 81 (2000) 747-768] and Tsutaya [J. London Math. Society 85 (2012) 142-164] that the number of An-types of the gauge groups of P is finite if n < ∞ and K is a finite complex. We show that the number of A∞-types of the gauge groups of P is infinite if K is a sphere and there are infinitely many P.

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U2 - 10.1112/jtopol/jtv025

DO - 10.1112/jtopol/jtv025

M3 - Article

VL - 9

SP - 181

EP - 191

JO - Journal of Topology

JF - Journal of Topology

SN - 1753-8416

IS - 1

M1 - jtv025

ER -