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We define centrally large subalgebras of simple unital C*-algebras,strengthening the definition of large subalgebras in previous work. We provethat if A is any infinite dimensional simple separable unital C*-algebra whichcontains a centrally large subalgebra with stable rank one, then A has stablerank one. We also prove that large subalgebras of crossed product type areautomatically centrally large. We use these results to prove that if X is acompact metric space which has a surjective continuous map to the Cantor set,and h is a minimal homeomorphism of X, then C* (Z, X, h) has stable rank one,regardless of the dimension of X or the mean dimension of h. In particular, theGiol-Kerr examples give crossed products with stable rank one but which are notstable under tensoring with the Jiang-Su algebra and are therefore notclassifiable in terms of the Elliott invariant.

Permanence of stable rank one for centrally large subalgebras and crossed products by minimal homeomorphisms