### Abstract

Given a fusion system F on a finite p-group P, where p is a prime, we show that the partially ordered set of isomorphism classes in F of chains of non-trivial subgroups of P, considered as topological space, is contractible, further generalising Symonds’, proof [Comment. Math. Helvet. 73 (1998) 400–405] of a conjecture of Webb [Comment. Math. Helvet. 66 (1991) 34–69; Arcata Conference on Representations of Finite Groups, part I, Proceedings of Symposia in Pure Mathematics 47 349–365] and its generalisation to non-trivial Brauer pairs associated with a p-block by Barker [J. Algebra 212 (1999) 460–465].

Original language | English |
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Pages (from-to) | 191-216 |

Number of pages | 26 |

Journal | Journal of the London Mathematical Society |

Volume | 98 |

Issue number | 1 |

Early online date | 13 Jun 2008 |

DOIs | |

Publication status | Published - Jan 2009 |

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## Cite this

Linckelmann, M. (2009). The orbit space of a fusion system is contractible.

*Journal of the London Mathematical Society*,*98*(1), 191-216. https://doi.org/10.1112/plms/pdn029