Analytic knots, satellites and the 4-ball genus

Abstract

Call a smooth knot (or smooth link) in the unit sphere in ${\mathbb{C}}^2$ analytic (respectively, smoothly analytic) if it bounds a complex curve (respectively, a smooth complex curve) in the complex ball. Let $K$ be a smoothly analytic knot. For a small tubular neighbourhood of $K$ we give a sharp lower bound for the 4-ball genus of analytic links $L$ contained in it.

revision, inaccuracies corrected, added in proof

References in corpus (3)

• Algebraic functions and closed braids
• Bounds for the Thurston-Bennequin number from Floer homology
• Envelopes of holomorphy and holomorphic discs

Cited by in corpus (1)

• Branched covers of quasipositive links and L-spaces