Cylindrical contact homology of subcritical Stein-fillable contact manifolds.(English)Zbl 1055.57036
We call a complex \(n\)-dimensional Stein domain subcritical if it admits a proper, strictly \(J\) (associated almost complex structure)-convex Morse function with finitely many critical points all having Morse index \(<n\). We call a contact manifold subcritical Stein-fillable if it is the boundary of some subcritical Stein domain with the induced contact structure. The contact homology of a contact manifold is defined by suitably counting punctured pseudoholomorphic spheres in its symplectization, which converge exponentially to “good” periodic Reeb orbits at punctures. In some cases, one can count only pseudoholomorphic cylinders, and thus define the cylindrical contact homology. In this paper, the author computes the cylindrical contact homology of subcritical Stein-fillable contact manifolds with vanishing first Chern class of the contact bundle. As a result, the contact homology of such a contact manifold recovers in a way the homology of the corresponding Stein domain.
Reviewer: Jih-Hsin Cheng (Taipei)
MSC:
| 57R17 | Symplectic and contact topology in high or arbitrary dimension |
| 57R65 | Surgery and handlebodies |
| 53D40 | Symplectic aspects of Floer homology and cohomology |
| 58C10 | Holomorphic maps on manifolds |
Cite
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