On manifolds satisfying stable systolic inequalities

Details On manifolds satisfying stable systolic inequalities On manifolds satisfying stable systolic inequalities

2007-08-20

arxiv.org/abs/0708.2589v2

Mathematics

Geometric Topology

15 pages; Theorem 1.4 is improved, the dependence on the intersection form is clearified

Scientific paper

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.

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