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

2010/02/23 by Lidman, Tye · 1 citation
#57M27 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1002.4389

Abstract

Ozsvath and Szabo construct a spectral sequence with E₂ term Λ^*(H¹(Y;Z))⊗ Z[U,U^-1] converging to HF^∞(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^∞(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^∞ with mod 2 coefficients when b₁ is 3 or 4.

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