Inverse semigroups associated with one-dimensional generalized solenoids

Homology and Matui’s Hk Conjecture for Groupoids on One-Dimensional Solenoids

“…Proof. By [18, Theorem 3.9], X is the phase space of a flow ϕ : X × R → X without a rest point so that G u is topologically isomorphic to the transformation groupoid X × ϕ R. Then, by [18,Proposition 3.14],…”

“…T of the Bratteli diagram B T . Moreover, the Bratteli diagram B T is stationary and the incidence matrix of B T is the adjacency matrix M of the onedimensional solenoid (X, f ) [18,Proposition 3.14]. We recall that the (i, j)-term of M is the number of edges from the vertex j in the kth level of B T to vertex i in the (k + 1)th level (see [3,6] for details).…”

Self-Similar Inverse Semigroups from Wieler Solenoids

“…Again, the proof of the following proposition is exactly the same as that of ( [22], Proposition 4.14), but we include it for completeness. Proposition 5.…”