6533b85bfe1ef96bd12ba2b2

RESEARCH PRODUCT

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

K. A. De RezendeO. Manzoli NetoGioia M. VagoMaria Alice Bertolim

subject

Lyapunov functionBetti numberHandle decompositionHandle decompositionHomology (mathematics)Betti's theoremManifoldTOPOLOGIA-GEOMETRIACombinatoricssymbols.namesakeOgasa invariantsymbolsBetti numbersConley index theoryGeometry and TopologyInvariant (mathematics)Mathematics::Symplectic GeometryConley indexMathematics

description

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.

yearjournalcountryeditionlanguage
2011-04-01Topology and its Applications
10.1016/j.topol.2011.01.021http://dx.doi.org/10.1016/j.topol.2011.01.021