Morse-Smale equations of non-saddle decompositions

International Conference on Topology and Its Applications, SEP 02-09, 2000, Ohrid, MACEDONIA
The notion of a non-saddle decomposition of a compact ANR is introduced. This notion extends that of a an attractor-repeller pair. Some cohomological properties of non-saddle decompositions are studied. In particular, some inequalities in the spirit of the Morse-Smale equations for attractor-repeller pairs are obtained. These inequalities involve the ranks of the cohomological Conley index and also of a new cohomological invariant introduced here. The notion of a cyclic Morse decomposition is also introduced and it is proved that this kind of decomposition admits filtrations by non-saddle sets. Finally, these filtrations are used to obtain Morse-Smale equations that generalize those of a Morse decomposition.
Depto. de Álgebra, Geometría y Topología
Fac. de Ciencias Matemáticas
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