Invariance of symplectic cohomology and twisted cotangent bundles over surfaces
We prove that symplectic cohomology for open convex symplectic manifolds is invariant when the symplectic form undergoes deformations which may be nonexact and noncompactly supported, provided one uses the correct local system of coefficients in Floer theory. As a sample application beyond the Liouv...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
30 July 2020
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| In: |
International journal of mathematics
Year: 2020, Volume: 31, Issue: 9, Pages: 1-48 |
| ISSN: | 1793-6519 |
| DOI: | 10.1142/S0129167X20500706 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1142/S0129167X20500706 Verlag, lizenzpflichtig, Volltext: https://www.worldscientific.com/doi/abs/10.1142/S0129167X20500706 
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| Author Notes: | Gabriele Benedetti, Alexander F. Ritter |
| Summary: | We prove that symplectic cohomology for open convex symplectic manifolds is invariant when the symplectic form undergoes deformations which may be nonexact and noncompactly supported, provided one uses the correct local system of coefficients in Floer theory. As a sample application beyond the Liouville setup, we describe in detail the symplectic cohomology for disc bundles in the twisted cotangent bundle of surfaces, and we deduce existence results for periodic magnetic geodesics on surfaces. In particular, we show the existence of geometrically distinct orbits by exploiting properties of the BV-operator on symplectic cohomology. |
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| Item Description: | Gesehen am 15.10.2020 |
| Physical Description: | Online Resource |
| ISSN: | 1793-6519 |
| DOI: | 10.1142/S0129167X20500706 |