Stable systolic inequalities and cohomology products

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dc.creatorBangert, Victor
dc.creatorKatz, Mikhail
dc.date2002-04-14
dc.date.accessioned2026-07-07T04:47:41Z
dc.date.available2026-07-07T04:47:41Z
dc.descriptionMultiplicative relations in the cohomology ring of a manifold impose constraints upon its stable systoles. Given a compact Riemannian manifold (X,g), its real homology H_*(X,R) is naturally endowed with the stable norm. Briefly, if h\in H_k(X,R) then the stable norm of h is the infimum of the Riemannian k-volumes of real cycles representing h. The stable k-systole is the minimum of the stable norm over nonzero elements in the lattice of integral classes in H_k(X,R). Relying on results from the geometry of numbers due to W. Banaszczyk, and extending work by M. Gromov and J. Hebda, we prove metric-independent inequalities for products of stable systoles, where the product can be as long as the real cup length of X.
dc.description26 pages. To appear in Communications on Pure and Applied Mathematics
dc.identifierhttps://arxiv.org/abs/math/0204181
dc.identifierhttp://arxiv.org/abs/math/0204181
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63814
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.subjectMetric Geometry
dc.subject53C23; 55Q15
dc.titleStable systolic inequalities and cohomology products
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