Flow-type suspension and homotopy suspension agree for attractor–repellor homotopy data. The connection maps associated in Conley index theory to an attractor–repellor decomposition with respect to the direct flow and its inverse are Spanier–Whitehead duals in the stably parallelizable context and are duals modulo a certain Thom construction in general.
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Octavian Cornea (2000) studied this question.
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