On the Infinity Flavor of Heegaard Floer Homology and the Integral Cohomology Ring

Details On the Infinity Flavor of Heegaard Floer Homology and the Integral Cohomology Ring On the Infinity Flavor of Heegaard Floer Homology and the Integral Cohomology Ring

2010-02-23

arxiv.org/abs/1002.4389v1

Mathematics

Geometric Topology

18 pages, 5 figures

Scientific paper

Ozsvath and Szabo construct a spectral sequence with E_2 term \Lambda^*(H^1(Y;Z))\otimes Z[U,U^{-1}] converging to HF^\infty(Y,s) for a torsion Spin^c structure s. They conjecture that the differentials are completely determined by the integral triple cup product form via a proposed formula. In this paper, we prove that HF^\infty(Y,s) is in fact determined by the integral cohomology ring when s is torsion. Furthermore, for torsion Spin^c structures, we give a complete calculation of HF^\infty with mod 2 coefficients when b_1 is 3 or 4.

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