A Twisted Tensor Product on symbolic dynamical Systems and the Ashley's Problem
Hastings, Harold M. and Silberger, S. and Weiss, M. T. and Wu, Y. (2001) A Twisted Tensor Product on symbolic dynamical Systems and the Ashley's Problem. Technical Report. Hofstra University.
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We define the notion of fiber bundle via a twisted tensor product on the transition matrices. We define the notion of topological conjugacy and shift equivalence in this bundle context and show that topological conjugacy implies shift equivalence. We show that the "Ashley system" S_A fits into our fiber bundle context. We introduce another system S_W, topologically conjugate to the full 2-shift, which has the same base space and fiber as the Ashley system, but is constructed with a different twisting. We show that S_A and S_W are shift equivalent but not bundle isomorphic.
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