Together with M. Boyle and D. Huang ( 2000), this paper gives an alternate development of the Huang classification of shifts of finite type up to flow equivalence, and provides additional functorial information, used to analyze the action of the mapping class group of the mapping torus of a shift of finite type on the isotopy futures group, which is introduced here. For a shift of finite type A, this group is isomorphic to the Bowen-Franks group cok (I-A). The action on the isotopy futures group of a subshift is the flow equivalence analogue of the dimension group representation. [References: 41]
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