SPLITTING FORMULAS FOR CERTAIN WALDHAUSEN NIL ...

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SPLITTING FORMULAS FOR CERTAIN WALDHAUSEN NIL-GROUPS. JEAN-FRANC¸OIS LAFONT AND IVONNE J. ORTIZ Abstract. We provide splitting formulas for certain Waldhausen Nil-groups. We focus on Waldhausen Nil-groups associated to acylindrical amalgamations Γ = G1∗HG2 of groups G1, G2 over a common subgroup H. For these amalga- mations, we explain how, provided G1, G2,Γ satisfy the Farrell-Jones isomor- phism conjecture, the Waldhausen Nil-groups NilW∗ (RH;R[G1 −H], R[G2 − H]) can be expressed as a direct sum of Nil-groups associated to a specific collection of virtually cyclic

• waldhausen nil
• geometry of group actions on trees
• relative assembly maps
• evc γ
• cokernel of the relative assembly map
• family of subgroups
• cyclic subgroups
• groups
• action
• group