The Growth Rate of Symplectic Homology and Affine Varieties
By Mark McLean. 2010
57 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7603858a3f6006f595f585bff413e0cd60e57eb8
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Legendrian fronts for affine varieties (2016, background): “In this line, algebraic geometers have been proving a wealth of significant results on the algebraic isomorphism types of affine complex varieties [26, 59, 73] but the underlying Stein structures are not quite understood; see [54, 55, 66] for progress in this direction.”