Relative Ends, l^2 Invariants and Property (T)

Details Relative Ends, l^2 Invariants and Property (T) Relative Ends, l^2 Invariants and Property (T)

2010-03-11

arxiv.org/abs/1003.2370v2

Mathematics

Group Theory

Scientific paper

We establish a splitting theorem for one-ended groups H 2 and the almost malnormal closure of H is a proper subgroup of G. This yields splitting theorems for groups G with non-trivial first l^2 Betti number (\beta^2_1(G)). We verify the Kropholler Conjecture for pairs H < G satisfying \beta^2_1(G) > \beta^2_1(H). We also prove that every n-dimensional Poincare duality (PD^n) group containing a PD^(n-1) group H with property (T) splits over a subgroup commensurable with H.

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