# Cohomology and asymptotic stability of 1-dimensional continua

@article{Athanassopoulos1991CohomologyAA, title={Cohomology and asymptotic stability of 1-dimensional continua}, author={Konstantin Athanassopoulos}, journal={manuscripta mathematica}, year={1991}, volume={72}, pages={415-423} }

We prove that a 1-dimensional continuum carrying a flow without singular points is homeomorphic to the unit circle if its first Čech cohomology group with integer coefficients is isomorphic to ℤ. As an application of this we obtain 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.

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