Journal of Symplectic Geometry

Volume 14 (2016)

Number 1

Four-ball genus bounds and a refinement of the Ozsváth–Szabó tau invariant

Pages: 305 – 323



Jennifer Hom (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Zhongtao Wu (Department of Mathematics, Chinese University of Hong Kong)


Based on work of Rasmussen, we construct a concordance invariant associated to the knot Floer complex, and exhibit examples in which this invariant gives arbitrarily better bounds on the 4-ball genus than the Ozsváth–Szabó $\tau$ invariant.

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