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We construct a Floer type boundary operator for generalised Morse-Smaledynamical systems on compact smooth manifolds by counting the number ofsuitable flow lines between closed (both homoclinic and periodic) orbits andisolated critical points. The same principle works for the discrete situationof general combinatorial vector fields, defined by Forman, on CW complexes. Wecan thus recover the $\mathbb{Z}_2$ homology of both smooth and discretestructures directly from the flow lines (V-paths) of our vector field.

Floer Homology: From Generalized Morse-Smale Dynamical Systems to Forman's Combinatorial Vector Fields