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Universität Augsburg
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Universität Augsburg
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Herr Daniel Räde
LMU
spricht am
Dienstag, 4. September 2018
um
10:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| The $k$-systole of a closed Riemannian manifold $(M,g)$ is an invariant that captures the 'size' of the $k$-dimensional homology of $M$. A classic question in systolic geometry is whether there are relations between different systoles, which hold for every possible choice of $g$, or if they are free to vary independently when changing the metric. It is, for example, a well known result due to C. Loewner that for every metric on the 2-Torus the length of the shortest noncontractible loop is bounded from above by a constant times the total volume. In this talk we will focus on complex projective space and ask whether or not it is possible to realize an arbitrary set $a_1,\ldots,a_n$ of positive real numbers as the systoles of $\mathbb{C}P^n$. We discuss techniques to modify systoles and present some partial results they provide in the general setting. Afterwards we focus on the case of $\mathbb{C}P^2$, where we are able to give a positive answer, stating and motivating general results on systolic freedom in the process. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Bernhard Hanke |