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We study invariants associated to Smale spaces obtained from an expandingendomorphism on a (closed connected Riemannian) flat manifold. Specifically,the relevant invariants are the $K$-theory of the associated $C^*$-algebras andPutnam's homology theory for Smale spaces. The latter is isomorphic to thegroupoid homology of the groupoids used to construct the $C^*$-algebras.

Invariants for the Smale space associated to an expanding endomorphism of a flat manifold