3/1/2023 0 Comments Minimal subshiftHowever, the conjugating maps change the symbolic sequences drastically. The unbounded case is proved by reducing to the bounded case via the map We prove simultaneously a type II version of our results. of the fact that for a minimal substitution with the nonempty minimal subshift X, there exist an alphabet Z and a primitive substitution on Z such that X is topolog-ically conjugate to X. We also prove a bounded finitely summable version of the form: for an integer. If and are not unitarily equivalent, wemust add a pair of correction terms to the right-hand side. For any piecewise smooth path with and unitarily equivalent we show that the integral of the 1-form. Furthermore, if Y nZ is another minimal subshift, then TF(X)0TF(Y)0if and only if X and Y are ip. More pre-cisely, if X nZ is a minimal subshift and TF(X) is the topological full group, then the commutator subgroup TF(X)0is an in nite nitely gen-erated simple amenable group. Then we show that for a sufficiently large half-integer: is a closed 1-form. Monod 18 on the topological full groups of minimal subshifts. Now, for in our manifold, any is given by an in as the derivative at along the curve in the manifold. Getzler in the -summable case) to consider the operator as a parameter in the Banach manifold,, so that spectral flow can be exhibited as the integral of a closed 1-form on this manifold. This integer, recovers the pairing of the -homology class with the -theory class. The spectral flow of this path (or ) is roughly speaking the net number of eigenvalues that pass through 0 in the positive direction as runs from 0 to 1. More precisely, we show that is a norm-continuous path of (bounded) self-adjoint Fredholm operators. The path is a “continuous” path of unbounded self-adjoint “Fredholm” operators. If is a unitary in the dense -subalgebra mentioned in (2) then where is a bounded self-adjoint operator. Abstract: An odd unbounded (respectively, -summable) Fredholm module for a unital Banach -algebra,, is a pair where is represented on the Hilbert space,, and is an unbounded self-adjoint operator on satisfying: (1) is compact (respectively, Trace, and (2) is a dense - subalgebra of.
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