The Growth Rate of Symplectic Homology and Affine Varieties
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Author(s)
McLean, Mark Robert Leonard
Date Issued
May 2012
Journal
Geometric and Functional Analysis
Publisher
SP Birkhäuser Verlag Basel
Citation
McLean, Mark. “The Growth Rate of Symplectic Homology and Affine Varieties.” Geometric and Functional Analysis 22, no. 2 (April 2012): 369–442.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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.
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DOI of Published Version
https://doi.org/10.1007/s00039-012-0158-7
