On the Heegaard Floer homology of a surface times a circle |
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Authors: | Stanislav Jabuka Thomas E Mark |
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Institution: | a University of Nevada, Reno, NV 89557, USA b University of Virginia, Charlottesville, VA 22904, USA |
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Abstract: | We make a detailed study of the Heegaard Floer homology of the product of a closed surface Σg of genus g with S1. We determine HF+(Σg×S1,s;C) completely in the case c1(s)=0, which for g?3 was previously unknown. We show that in this case HF∞ is closely related to the cohomology of the total space of a certain circle bundle over the Jacobian torus of Σg, and furthermore that HF+(Σg×S1,s;Z) contains nontrivial 2-torsion whenever g?3 and c1(s)=0. This is the first example known to the authors of torsion in Z-coefficient Heegaard Floer homology. Our methods also give new information on the action of H1(Σg×S1) on HF+(Σg×S1,s) when c1(s) is nonzero. |
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Keywords: | Heegaard Floer homology Gauge theory Three-manifolds |
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