On Suspensions Over Gradient-Like Diffeomorphisms of Surfaces with Three Periodic Orbits
摘要
S. Smale showed that suspensions over conjugate diffeomorphisms are topologically equivalent. Under certain assumptions, the conjugacy of diffeomorphisms is equivalent to the equivalence of suspensions. We show that this criterion holds for gradient-like diffeomorphisms with three periodic orbits on arbitrary orientable surfaces, prove that 3-manifolds admitting suspensions over such diffeomorphisms are small Seifert manifolds, and calculate the homology groups of these manifolds and the number of equivalence classes of flows on each admissible Seifert manifold.