## Twin Buildings and Applications to S-Arithmetic GroupsThis book is addressed to mathematicians and advanced students interested in buildings, groups and their interplay. Its first part introduces - presupposing good knowledge of ordinary buildings - the theory of twin buildings, discusses its group-theoretic background (twin BN-pairs), investigates geometric aspects of twin buildings and applies them to determine finiteness properties of certain S-arithmetic groups. This application depends on topological properties of some subcomplexes of spherical buildings. The background of this problem, some examples and the complete solution for all "sufficiently large" classical buildings are covered in detail in the second part of the book. |

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### Contents

Table of contents | 1 |

Groups acting on twin buildings | 11 |

Homotopy properties of Aa | 56 |

Copyright | |

3 other sections not shown

### Common terms and phrases

A+,A_ acting strongly transitively algebraic assume Bruhat-Tits building building associated building of type chamber Chapter Chevalley group choose classical Cn building coconvex containing convex convex hull coprojections Corollary Coxeter complex Coxeter group Coxeter system deduced defined Definition Denote dimF dimt E(c+,c_ E+,E_ element Example exists filtration finiteness properties flag complex function field fundamental domain group G group theoretic Hence homeomorphic homotopy implies infinite isomorphic isotropic lines Kac-Moody groups Lemma Lemma 11 Lemma 32 m-gon minimal Moufang obtain opposite parabolic subgroups Proposition 13 Recall Remark RGD-system RGD3 root datum root groups S-arithmetic groups satisfying simplex simplices simplicial complex space spherical buildings StabG(E statement subcomplexes subgroup TBN1 TBN2 Theorem theory thick twin apartment twin BN-pair twin buildings vertex Weyl group x+(w