Search results for "Conley index theory"

showing 2 items of 2 documents

On the variations of the Betti numbers of regular levels of Morse flows

2011

Abstract We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Betti numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z p Z with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds.

Lyapunov functionBetti numberHandle decompositionHandle decompositionHomology (mathematics)Betti's theoremManifoldTOPOLOGIA-GEOMETRIACombinatoricssymbols.namesakeOgasa invariantsymbolsBetti numbersConley index theoryGeometry and TopologyInvariant (mathematics)Mathematics::Symplectic GeometryConley indexMathematicsTopology and its Applications
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Lyapunov graphs for circle valued functions

2018

International audience; Conley index theory is used to obtain results for flows associated to circular Lyapunov functions defined on general compact smooth n-manifolds. This is done in terms of their underlying circular Lyapunov digraphs, which are generalizations of Morse digraphs, by extensively studying their combinatorics, invariants and realizability.

Lyapunov functionNovikov theoryPure mathematicsMathematics::Dynamical Systems010102 general mathematicsTEORIA DO ÍNDICEMorse code01 natural scienceslaw.inventionLyapunov graphs010101 applied mathematicssymbols.namesakeMorse functions[MATH.MATH-GN]Mathematics [math]/General Topology [math.GN]lawRealizabilitysymbolsGeometry and TopologyConley index theory0101 mathematicsMathematics::Symplectic GeometryGeneric circularMSC: primary 37B30 37B35 37D15 secondary 37E35MathematicsConley index
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