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...

In Bartels–Lück [1] we introduced the concept of transfer reducible groups with respect to a family of subgroups. This definition is somewhat technical and recalled as Definition 0.4 below. We showed that groups that are transfer reducible over the family of virtually cyclic subgroups satisfy the Farrell–Jones Conjecture with coefficients in an additive category. For further explanations about ...

We examine the notion of α-strong singularity for subfactors of a II1 factor, which is a metric quantity that relates the distance of a unitary to a subalgebra with the distance between that subalgebra and its unitary conjugate. Using work of Popa, Sinclair, and Smith, we show that there exists an absolute constant 0 < c < 1 such that all subfactors are c-strongly singular. Under additional hyp...

We provide a new proof of Brylawski’s formula for the Tutte polynomial of the tensor product of two matroids. Our proof involves extending Tutte’s formula, expressing the Tutte polynomial using a calculus of activities, to all polynomials involved in Brylawski’s formula. The approach presented here may be used to show a signed generalization of Brylawski’s formula, which may be used to compute ...