On Manifolds Satisfying Stable Systolic Inequalities

Abstract

We show that for closed orientable manifolds the k-dimensional stable systole admits a metric-independent volume bound if and only if there are cohomology classes of degree k that generate cohomology in top-degree. Moreover, it turns out that in the nonorientable case such a bound does not exist for stable systoles of dimension at least two. Additionally, we prove that the stable systolic constant depends only on the image of the fundamental class in a suitable Eilenberg-MacLane space. Consequently, the stable k-systolic constant is completely determined by the multilinear intersection form on k-dimensional cohomology.

Cite this paper

@inproceedings{Brunnbauer2008OnMS, title={On Manifolds Satisfying Stable Systolic Inequalities}, author={Michael Brunnbauer}, year={2008} }