TY - JOUR

T1 - Stable Systolic Inequalities and Cohomology Products

AU - Bangert, Victor

AU - Katz, Mikhail

PY - 2003/7

Y1 - 2003/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=2442463357&partnerID=8YFLogxK

U2 - 10.1002/cpa.10082

DO - 10.1002/cpa.10082

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:2442463357

SN - 0010-3640

VL - 56

SP - 979

EP - 997

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

IS - 7

ER -