A global two-dimensional version of Smale’s cancellation theorem via spectral sequences
Maria Alice Bertolim, Dahisy V. S. Lima, Margarida Pinheiro Mello, Ketty Abaroa de Rezende, Mariana R. da Silveira · Ergodic Theory and Dynamical Systems · 2015
In this article, Conley’s connection matrix theory and a spectral sequence analysis of a filtered Morse chain complex $(C,{\rm\Delta})$ are used to study global continuation results for flows on surfaces. The briefly described unfoldings of Lyapunov graphs have been proved to be a well-suited combinatorial tool to keep track of continuations. The novelty herein is a global dynamical cancellation theorem inferred from the differentials of the spectral sequence $(E^{r},d^{r})$ . The local version of this theorem relates differentials $d^{r}$ of the $r$ th page $E^{r}$ to Smale’s theorem on cancellation of critical points.