Contact structures and geometric topology

TL;DR

This survey explores contact open books and contact Dehn surgery, discussing their relationship and applications in contact and symplectic topology, including monodromy, fibred links, and Legendrian knots.

Contribution

It provides a comprehensive overview of contact open books and Dehn surgery, highlighting their interrelation and various recent applications in geometric topology.

Findings

Relationship between contact open books and Dehn surgery elucidated

Applications include monodromy of Stein fillable manifolds and detection of Legendrian knots

Construction of symplectic caps and proof of Harer's conjecture discussed

Abstract

This is a survey on contact open books and contact Dehn surgery. The relation between these two concepts is discussed, and various applications are sketched, e.g. the monodromy of Stein fillable contact 3-manifolds, the Giroux-Goodman proof of Harer's conjecture on fibred links, construction of symplectic caps to fillings (Eliashberg, Etnyre), and detection of non-loose Legendrian knots with the help of contact surgery.