Creating semiflows on simplicial complexes from combinatorial vector fields

Combinatorial vector fields on simplicial complexes as introduced by Robin Forman have found numerous and varied applications in recent years. Yet, their relationship to classical dynamical systems has been less clear. In work it was shown that for every combinatorial field a finite complex one can construct multivalued discrete-time system the underlying polytope X which exhibits same dynamics flow sense of Conley index theory. However, Forman's original description flows appears motivated more directly concept flows, i.e., continuous-time systems. this paper, is semiflow field. The equivalence behavior established Conley-Morse graphs uses tiling topological space makes possible isolating blocks all involved isolated invariant sets based purely information.