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Detection of L-Space Knots by Their Four-Manifold Traces

A result in low-dimensional topology showing that the 0-trace of a knot (the 4-manifold formed by attaching a 0-framed 2-handle to the 4-ball) determines the knot whenever it is an L-space knot. The argument establishes that a single trace already detects the L-space property and the knot's genus, and that two L-space knots sharing a 0-surgery must coincide, linking symplectic Floer homology of the monodromy to Heegaard Floer homology of the mapping torus and using pseudo-Anosov rigidity.

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L-SPACES AND KNOT TRACES JOHN A. BALDWIN AND STEVEN SIVEK Abstract. There has been a great deal of

This paper studies which knots in the 3-sphere are detected by their n-traces (the smooth 4-manifold obtained by attaching an n-framed 2-handle to the 4-ball along the knot) as a four-dimensional ana…