Stable Systolic Inequalities and Cohomology Products

Victor Bangert, Mikhail Katz

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25 Scopus citations


Multiplicative 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 ∈ Hk (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 Hk (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.

Original languageEnglish
Pages (from-to)979-997
Number of pages19
JournalCommunications on Pure and Applied Mathematics
Issue number7
StatePublished - Jul 2003


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