### Abstract

Let F → X → B be a fibre bundle with structure group G, where B is (d - 1)-connected and of finite dimension, d ≥ 1. We prove that the strong L-S category of X is less than or equal to m+ dim B/d, if F has a cone decomposition of length m under a compatibility condition with the action of G on F. This gives a consistent prospect to determine the L-S category of non-simply connected Lie groups. For example, we obtain cat (PU(n)) ≤ 3(n - 1) for all n ≥ 1, which might be best possible, since we have cat (PU(p^{r})) = 3(p^{r} - 1) for any prime p and r ≥ 1. Similarly, we obtain the L-S category of SO (n) for n ≤ 9 and PO(8). We remark that all the above Lie groups satisfy the Ganea conjecture on L-S category.

Original language | English |
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Pages (from-to) | 111-123 |

Number of pages | 13 |

Journal | Topology and its Applications |

Volume | 150 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - May 14 2005 |

### All Science Journal Classification (ASJC) codes

- Geometry and Topology

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## Cite this

*Topology and its Applications*,

*150*(1-3), 111-123. https://doi.org/10.1016/j.topol.2004.11.006