Four-dimensional aspects of tight contact 3-manifolds.
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- Record sourced from PubMed, PMID 34035169.
- Also identified by DOI 10.1073/pnas.2025436118 and PMC identifier 8179132.
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Abstract
We conjecture a four-dimensional characterization of tightness: A contact structure on a 3-manifold Y is tight if and only if a slice-Bennequin inequality holds for smoothly embedded surfaces in [Formula: see text] An affirmative answer to our conjecture would imply an analogue of the Milnor conjecture for torus knots: If a fibered link L induces a tight contact structure on Y, then its fiber surface maximizes the Euler characteristic among all surfaces in [Formula: see text] with boundary L. We provide evidence for both conjectures by proving them for contact structures with nonvanishing Ozsváth-Szabó contact invariant.