Proves the integer-coefficient surgery exact triangle in monopole Floer homology and derives a spectral sequence from odd Khovanov homology to the monopole Floer homology of the double branched cover, solving the Ozsváth-Rasmussen-Szabó conjecture.
Bordered Floer homology with integral coefficients for manifolds with torus boundary
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abstract
We provide a combinatorial definition of a bordered Floer theory with $\mathbb Z$ coefficients for manifolds with torus boundary. Our bordered Floer structures recover the combinatorial Heegaard Floer homology defined by Ozsv\'ath, Stipsicz, and Szab\'o.
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2026 1verdicts
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Monopole triangle over integers
Proves the integer-coefficient surgery exact triangle in monopole Floer homology and derives a spectral sequence from odd Khovanov homology to the monopole Floer homology of the double branched cover, solving the Ozsváth-Rasmussen-Szabó conjecture.