A note on generalized Thurston--Bennequin inequalities

TL;DR

This paper extends Thurston--Bennequin inequalities to links in S^3 using Bauer--Furuta invariants, providing new bounds related to contact topology and 4-manifold embeddings.

Contribution

It introduces a generalized Thurston--Bennequin inequality leveraging Bauer--Furuta invariants for contact 4-manifolds and derives an adjunction inequality for embedded surfaces.

Findings

Established a new inequality for links in S^3

Derived an adjunction inequality for surfaces in 4-manifolds

Connected contact topology with Bauer--Furuta invariants

Abstract

We give a generalized Thurston--Bennequin-type inequality for links in $S^3$ using a Bauer--Furuta-type invariant for 4-manifolds with contact boundary. As a special case, we also give an adjunction inequality for smoothly embedded orientable surfaces with negative intersection in a closed oriented smooth 4-manifold whose non-equivariant Bauer--Furuta invariant is non-zero.