Conley's spectral sequence via the sweeping algorithm (Q989093)

This paper presents an algorithm to find a sequence of connection matrices over a field \(\mathbb{F}\) which determine the spectral sequence \((E^r,d^r)\) associated to a filtered Morse-Conley chain complex from a connection matrix \(\Delta\) over a field \(\mathbb{F}\). This extends the algorithm from the case where \(\Delta\) is a connection matrix over \(\mathbb{Z}\) studied by \textit{O. Cornea, K. A. de Rezende}, and \textit{M. R. da Silveira} [Ergodic Theory Dyn. Syst. 30, No. 4, 1009--1054 (2010; Zbl 1210.37009)]. In the algorithm, a sequence of connection matrices \(\Delta^0=\Delta, \Delta^1, \dots, \Delta^R\) is constructed where \(\Delta^r\) is similar to \(\Delta^{r-1}\). The authors prove that the last matrix \(\Delta^R\) is integral even though some of the intermediate matrices might not be. Results are also obtained for the intermediate matrices \(\Delta^r\) and the change-of-basis matrices from the similarities.