The isomorphism conjecture in $L$-theory: graphs of groups
Copyright policy )The isomorphism conjecture in $L$-theory: graphs of groups
We study the Fibered Isomorphism Conjecture of Farrell and Jones in L-theory for groups acting on trees. In several cases we prove the conjecture. This includes wreath products of abelian groups and free metabelian groups. We also deduce the conjecture in pseudoisotopy theory for these groups. Finally in B of Theorem 1.1 we prove the L-theory version of [[7], Theorem 1.2].
20 pages. AMSLATEX file, updated and revised incorporating referee's suggestions and simplified notations
\(L\)-theory of group rings, Farrell-Jones isomorphism conjecture, $L$-theory, 19G24, 19G24, 19J25 (Primary), 55N91 (Secondary), Equivariant homology and cohomology in algebraic topology, 19J25, surgery group, K-Theory and Homology (math.KT), Geometric Topology (math.GT), Borel conjecture, fibered isomorphism conjecture, pseudoisotopy groups, 55N91, L-theory, Mathematics - Geometric Topology, geometric topology, Mathematics - K-Theory and Homology, FOS: Mathematics, graph of groups, group action on trees, Group action on trees, Surgery obstructions (\(K\)-theoretic aspects)
\(L\)-theory of group rings, Farrell-Jones isomorphism conjecture, $L$-theory, 19G24, 19G24, 19J25 (Primary), 55N91 (Secondary), Equivariant homology and cohomology in algebraic topology, 19J25, surgery group, K-Theory and Homology (math.KT), Geometric Topology (math.GT), Borel conjecture, fibered isomorphism conjecture, pseudoisotopy groups, 55N91, L-theory, Mathematics - Geometric Topology, geometric topology, Mathematics - K-Theory and Homology, FOS: Mathematics, graph of groups, group action on trees, Group action on trees, Surgery obstructions (\(K\)-theoretic aspects)
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