The growth rate of symplectic homology and affine varieties

Details The growth rate of symplectic homology and affine varieties The growth rate of symplectic homology and affine varieties

2010-11-11

arxiv.org/abs/1011.2542v4

Mathematics

Symplectic Geometry

79 pages, 3 figures. Corrected mistakes and changed the introduction

Scientific paper

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.

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