On manifolds satisfying stable systolic inequalities |
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Authors: | Michael Brunnbauer |
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Institution: | 1.Mathematisches Institut, Ludwig-Maximilians-Universit?t München,München,Germany |
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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–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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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 53C23 53C20 |
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