## Splitting assembly maps for arithmetic groups with large actions at infinity |

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### Contents

Homotopy Theoretic Preliminaries | 5 |

Symmetric Spaces Arithmetic Groups | 14 |

Assembly in Algebraic Jftheory | 25 |

Copyright | |

9 other sections not shown

### Common terms and phrases

analogues arithmetic group arithmetic subgroup assembly map asymptotic Borel subgroup Bounded Saturation boundedly saturated sets Cech homology Cech-acyclic cellular decompositions choice closure cofinal compactification connected construction contained contractible converging coordinate Corollary corresponding CovX CovY de(B defined Definition denote derived decomposition e(Po equivariant eX(M Example fiber fibration finite rigid coverings flat functor fundamental domain given Hausdorff holim N_ homeomorphic homotopy limits hyperbolic induced intersection isomorphism lattice left cofinal left filtering Lemma Lie group morphisms nerve nilpotent group notation Novikov conjecture open coverings open neighborhood open sets open subset OrdY parabolic subgroup projection Proof of Theorem proper parabolic Proposition Q-subgroup quasi-isometry quotient R-rank Recall right action Satake compactifications semi-simple sequence simplicial set spectra spectrum standard parabolic Steenrod strata stratum subgroup of G subspace symmetric space T-invariant metric topology torsion-free unipotent Vn(B weak equivalence weak homotopy equivalence Weyl chamber