On the Heegaard Floer Homology of a Surface times a Circle
نویسنده
چکیده
We make a detailed study of the Heegaard Floer homology of the product of a closed surface Σg of genus g with S. We determine HF(Σg × S, 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 a the total space of a certain circle bundle over the Jacobian torus of Σg, and furthermore that HF(Σg ×S, 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 × S) on HF(Σg × S, s) when c1(s) is nonzero.
منابع مشابه
The Heegaard Floer Homology of a Surface times a Circle
We calculate the Heegaard Floer homology groups ĤF (Y, s0), HF (Y, s0) and HF∞(Y, s0) for Y the product of a genus g surface with a circle and s0 the torsion spin c structure. This has previously been calculated by Peter Ozsváth and Zoltán Szabó only for the cases of g = 0, 1, 2 (see [3, 5, 8] respectively).
متن کاملOn the Heegaard Floer Homology of a Surface times a Circle
We make a detailed study of the Heegaard Floer homology of the product of a closed surface Σg of genus g with S . We determine HF(Σg × S , 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 a the total space of a certain circle bundle over the Jacobian torus of Σg, and furthermore that HF (Σg ×S , ...
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