Mathematische Annalen

, 342:951 | Cite as

On manifolds satisfying stable systolic inequalities

  • Michael BrunnbauerEmail author


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–Mac Lane space. Consequently, the stable k-systolic constant is completely determined by the multilinear intersection form on k-dimensional cohomology.

Mathematics Subject Classification (2000)

53C23 53C20 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Mathematisches Institut, Ludwig-Maximilians-Universität MünchenMünchenGermany

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