Relative Symplectic Caps, 4-Genus And Fibered Knots

TL;DR

This paper develops relative symplectic capping techniques and applies them to analyze the 4-genus of knots, providing new insights into their symplectic and contact geometric properties.

Contribution

It introduces relative symplectic capping theorems and uses them to study the 4-genus and fibered knots in the context of Stein fillability.

Findings

Established relative symplectic capping results.

Connected Stein fillability with knot genus.

Provided criteria for fibered knots in symplectic topology.

Abstract

We prove relative versions of the symplectic capping theorem and sufficiency of Giroux's criterion for Stein fillability and use these to study the 4-genus of knots.