Search results for "Handle decomposition"

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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Round-handle decomposition ofS2×S1

2007

A round-handle decomposition is associated with a non-singular Morse–Smale flow on 3-manifolds prime to S 2× S 1. This decomposition has been built only for the 3-sphere S 3. In this paper we obtain the round-handle decomposition of non-singular Morse–Smale flows on S 2× S 1, in order to get all the different fattened round handles in this manifold. Some of them include non-separating boundary components that induce the topology of the links of periodic orbits.

Pure mathematicsHandle decompositionGeneral MathematicsBoundary (topology)Morse–Smale systemTopologyPrime (order theory)ManifoldComputer Science ApplicationsFlow (mathematics)Decomposition (computer science)Mathematics::Symplectic GeometryTopology (chemistry)MathematicsDynamical Systems
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