Lima, D. V. S.
Manzoli Neto, O.
de Rezende, K. A.
Total Authors: 3
 Univ Fed ABC, CMCC, Santo Andre, SP - Brazil
 Univ Sao Paulo, ICMC, Sao Carlos, SP - Brazil
 Univ Estadual Campinas, IMECC, Campinas, SP - Brazil
Total Affiliations: 3
Web of Science Citations:
In this article, we use Conley Index Theory to set up a framework to associate topological-dynamical invariants to a Morse-Bott flow in a neighborhood of a critical manifold. Isolating blocks N for a critical manifold S are characterized in terms of conditions on the ranks of its homology Conley index. The necessity of these conditions follows from the generalized Morse-Bott inequalities for isolating blocks. Morse-Bott semi-graphs turn out to be a useful combinatorial device to record these topological conditions. One goal is to verify that these conditions when imposed on an n-abstract Morse-Bott semi-graph are sufficient for its realization. This is attained by introducing Morse-Bott handle surgeries in order to construct isolating blocks for critical manifolds in dimensions 2 and 3, and for a large class in higher dimensions. Stronger results are obtained in dimensions 2 and 3 where necessary and sufficient conditions for a Morse-Bott graph to be associated to a Morse-Bott flow on some manifold M are determined. (AU)