The Growth Rate of Symplectic Homology and Affine Varieties
We will show that the cotangent bundle of a manifold whose free loopspace homology grows exponentially is not symplectomorphic to any smooth affine variety. We will also show that the unit cotangent bundle of such a manifold is not Stein fillable by a Stein domain whose completion is symplectomorphi...
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| Format: | Article |
| Language: | English |
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SP Birkhäuser Verlag Basel
2017
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| Online Access: | http://hdl.handle.net/1721.1/106919 |
| _version_ | 1826193566180835328 |
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| author | McLean, Mark Robert Leonard |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics McLean, Mark Robert Leonard |
| author_sort | McLean, Mark Robert Leonard |
| collection | MIT |
| description | We will show that the cotangent bundle of a manifold whose free loopspace homology grows exponentially is not symplectomorphic to any smooth affine variety. We will also show that the unit cotangent bundle of such a manifold is not Stein fillable by a Stein domain whose completion is symplectomorphic to a smooth affine variety. For instance, these results hold for end connect sums of simply connected manifolds whose cohomology with coefficients in some field has at least two generators. We use an invariant called the growth rate of symplectic homology to prove this result. |
| first_indexed | 2024-09-23T09:41:08Z |
| format | Article |
| id | mit-1721.1/106919 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:41:08Z |
| publishDate | 2017 |
| publisher | SP Birkhäuser Verlag Basel |
| record_format | dspace |
| spelling | mit-1721.1/1069192022-09-26T13:07:00Z The Growth Rate of Symplectic Homology and Affine Varieties McLean, Mark Robert Leonard Massachusetts Institute of Technology. Department of Mathematics McLean, Mark Robert Leonard We will show that the cotangent bundle of a manifold whose free loopspace homology grows exponentially is not symplectomorphic to any smooth affine variety. We will also show that the unit cotangent bundle of such a manifold is not Stein fillable by a Stein domain whose completion is symplectomorphic to a smooth affine variety. For instance, these results hold for end connect sums of simply connected manifolds whose cohomology with coefficients in some field has at least two generators. We use an invariant called the growth rate of symplectic homology to prove this result. National Science Foundation (U.S.) (grant DMS-1005365) 2017-02-10T22:29:15Z 2017-02-10T22:29:15Z 2012-05 2012-01 2016-08-18T15:40:18Z Article http://purl.org/eprint/type/JournalArticle 1016-443X 1420-8970 http://hdl.handle.net/1721.1/106919 McLean, Mark. “The Growth Rate of Symplectic Homology and Affine Varieties.” Geometric and Functional Analysis 22, no. 2 (April 2012): 369–442. en http://dx.doi.org/10.1007/s00039-012-0158-7 Geometric and Functional Analysis Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer Basel AG application/pdf SP Birkhäuser Verlag Basel SP Birkhäuser Verlag Basel |
| spellingShingle | McLean, Mark Robert Leonard The Growth Rate of Symplectic Homology and Affine Varieties |
| title | The Growth Rate of Symplectic Homology and Affine Varieties |
| title_full | The Growth Rate of Symplectic Homology and Affine Varieties |
| title_fullStr | The Growth Rate of Symplectic Homology and Affine Varieties |
| title_full_unstemmed | The Growth Rate of Symplectic Homology and Affine Varieties |
| title_short | The Growth Rate of Symplectic Homology and Affine Varieties |
| title_sort | growth rate of symplectic homology and affine varieties |
| url | http://hdl.handle.net/1721.1/106919 |
| work_keys_str_mv | AT mcleanmarkrobertleonard thegrowthrateofsymplectichomologyandaffinevarieties AT mcleanmarkrobertleonard growthrateofsymplectichomologyandaffinevarieties |