Symplectic isotopy on non-minimal ruled surfaces

TL;DR

This paper investigates the symplectic isotopy problem on non-minimal ruled surfaces, demonstrating stability properties and identifying new topological generators beyond known Lagrangian Dehn twists.

Contribution

It establishes the stability of symplectic diffeomorphisms on blown-up irrational ruled surfaces and uncovers novel topological generators of their symplectomorphism groups.

Findings

Proves stability of symplectic diffeomorphisms on blown-up irrational ruled surfaces.

Identifies new topological generators of the symplectomorphism group.

Detects generators different from Lagrangian Dehn twists.

Abstract

We prove the stability of $Symp(X,\omega)\cap Diff_0(X)$ for a one-point blow-up of irrational ruled surfaces and study their topological colimit. Non-trivial generators of $\pi_0[Symp(X,\omega)\cap Diff_0(X)]$ that differ from Lagrangian Dehn twists are detected.