Stable systolic inequalities and cohomology products
Abstract
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\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.
Keywords
Cite
@article{arxiv.math/0204181,
title = {Stable systolic inequalities and cohomology products},
author = {Victor Bangert and Mikhail Katz},
journal= {arXiv preprint arXiv:math/0204181},
year = {2007}
}
Comments
26 pages. To appear in Communications on Pure and Applied Mathematics