Cohomology and asymptotic stability of 1-dimensional continua (Q1178749)

The main result is that if the first Čech cohomology group with integer coefficients is isomorphic to \(\mathbb{Z}\), then, a 1-dimensional continuum carrying a flow without singular points is isomorphic to the unit circle. An application is that an asymptotically stable invariant 1- dimensional continuum of a flow on a locally compact ANR, which does not contain singular points, must be a periodic orbit.