JournalscmhVol. 88, No. 4pp. 875–898

On the infinity flavor of Heegaard Floer homology and the integral cohomology ring

  • Tye Lidman

    The University of Texas at Austin, USA
On the infinity flavor of Heegaard Floer homology and the integral cohomology ring cover
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Abstract

For a three-manifold YY and torsion Spinc\mathrm{Spin}^c structure s\mathfrak{s}, Ozsváth and Szabóconstruct a spectral sequence with E2E^2 term an exterior algebra over H1(Y;Z)H^1(Y;\mathbb{Z}) converging to HF(Y,s)H F^\infty(Y,\mathfrak{s}). They conjecture that the differentials are completely determined by the integral triple cup product form. In this paper, we prove that HF(Y,s)H\hskip-2pt F^\infty(Y,\mathfrak{s}) is in fact determined by the cohomology ring when s\mathfrak{s} is torsion. Furthermore, we give a complete calculation of such HF(Y,s)HF^\infty(Y,\mathfrak{s}), with mod 2 coefficients, in the case where b1(Y)b_1(Y) is 3 or 4.

Cite this article

Tye Lidman, On the infinity flavor of Heegaard Floer homology and the integral cohomology ring. Comment. Math. Helv. 88 (2013), no. 4, pp. 875–898

DOI 10.4171/CMH/306