6533b7d0fe1ef96bd125af1b

RESEARCH PRODUCT

Minimal Morse flows on compact manifolds

Maria Alice BertolimK. A. De RezendeGioia M. Vago

subject

Discrete mathematicsLyapunov functionTopological complexityBoundary (topology)Type (model theory)Morse codeManifoldLyapunov graphslaw.inventionsymbols.namesakePoincaré–Hopf inequalitieslawEuler's formulasymbolsGravitational singularityGeometry and TopologyMathematics::Symplectic GeometryConley indexMathematics

description

Abstract In this paper we prove, using the Poincare–Hopf inequalities, that a minimal number of non-degenerate singularities can be computed in terms only of abstract homological boundary information. Furthermore, this minimal number can be realized on some manifold with non-empty boundary satisfying the abstract homological boundary information. In fact, we present all possible indices and types (connecting or disconnecting) of singularities realizing this minimal number. The Euler characteristics of all manifolds realizing this minimal number are obtained and the associated Lyapunov graphs of Morse type are described and shown to have the lowest topological complexity.

yearjournalcountryeditionlanguage
2006-12-01Topology and its Applications
10.1016/j.topol.2006.03.005http://dx.doi.org/10.1016/j.topol.2006.03.005