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＜Doctoral Thesis＞
Stable systolic category of the product of spheres
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| Abstract | In this paper, a manifold is assumed to be closed, connected, orientable and smooth. The systole of a manifold M is the least length of non-contractible closed loops in M. One can generalize this conc...ept to the least volume of k?dimensional nonzero homology classes, so called as the homology systole. Now we can imagine such systoles have some kind of relations with the entire volume of M, and it is natural to ask what kind of relationship exists. As an answer, Gromov proved a theorem that says that the existence of non-trivial cup product implies the existence of the stable isosystolic inequality as follows.show more |
| Table of Contents | Introduction Acknowledgements Table of Contents 1 Stable systolic category 2 Preliminaries on stable systoles 3 Calculation by dimension and constructing metrics 4 Invariance under rational equivalences References |
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| Created Date | 2013.07.12 |
| Modified Date | 2023.11.21 |