For any finite dimensional C∗-algebra A , we give an endomorphism Φ of the hyperfinite II1 factor R of finite Jones index such that: ∀ k ∈ N, Φk(R)′ ∩R = ⊗kA. The Jones index [R : Φ(R)] = (rank (A)), here rank (A) is the dimension of the maximal abelian subalgebra of A.

We investigate when Isomorphism Conjectures, such as the ones due to Baum-Connes, Bost and Farrell-Jones, are stable under colimits of groups over directed sets (with not necessarily injective structure maps). We show in particular that both the K-theoretic Farrell-Jones Conjecture and the Bost Conjecture with coefficients hold for those groups for which Higson, Lafforgue and Skandalis have dis...

For a closed n–braid L with a full positive twist and with l negative crossings, 0 ≤ l ≤ n, we determine the first n− l+ 1 terms of the Jones polynomial VL(t). We show that VL(t) satisfies a braid index constraint, which is a gap of length at least n − l between the first two nonzero coefficients of (1−t)VL(t). For a closed positive n–braid with a full positive twist, we extend our results to t...