The Growth Rate of Symplectic Homology and Affine Varieties

Mark McLean

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)369-442
Number of pages73
JournalGeometric and Functional Analysis
Issue number2
Publication statusPublished - Apr 2012


  • symplectic homology
  • growth rate
  • affine variety
  • 53D35
  • 53D40


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