Local systems on the free loop space and finiteness of the Hofer-Zehnder capacity
In this article we examine under which conditions symplectic homology with local coefficients of a unit disk bundle D^*MD∗MD^*M vanishes. For instance this is the case if the Hurewicz map \pi _2(M)\rightarrow H_2(M;{\mathbb {Z}})π2(M)→H2(M;Z)\pi _2(M)\rightarrow H_2(M;{\mathbb {Z}}) is nonzero. As a...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2017
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| In: |
Mathematische Annalen
Year: 2016, Volume: 367, Issue: 3/4, Pages: 1403-1428 |
| ISSN: | 1432-1807 |
| DOI: | 10.1007/s00208-016-1401-6 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1007/s00208-016-1401-6 Verlag, Volltext: https://link.springer.com/article/10.1007/s00208-016-1401-6 
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| Author Notes: | Peter Albers, Urs Frauenfelder, Alexandru Oancea |
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| 520 | |a In this article we examine under which conditions symplectic homology with local coefficients of a unit disk bundle D^*MD∗MD^*M vanishes. For instance this is the case if the Hurewicz map \pi _2(M)\rightarrow H_2(M;{\mathbb {Z}})π2(M)→H2(M;Z)\pi _2(M)\rightarrow H_2(M;{\mathbb {Z}}) is nonzero. As an application we prove finiteness of the \pi _1π1\pi _1-sensitive Hofer-Zehnder capacity of unit disk bundles in these cases. We also prove uniruledness for such cotangent bundles. Moreover, we find an obstruction to the existence of H-space structures on general topological spaces, formulated in terms of local systems. | ||
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