Geometric and Functional Analysis

, Volume 22, Issue 2, pp 369–442 | Cite as

The Growth Rate of Symplectic Homology and Affine Varieties

  • Mark McLeanEmail author


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.

Keywords and phrases

Symplectic homology growth rate affine variety 

2010 Mathematics Subject Classification

53D35 53D40 


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© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of MathematicsMITCambridgeUSA

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