Chambers in the symplectic cone and stability of symplectomorphism group for ruled surface

2022/02/14 by Buse, Olguta, Li, Jun
#FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2202.06795

Abstract

We continue our previous work to prove that for any non-minimal ruled surface (M,ω), the stability under symplectic deformations of π₀, π₁ of Symp(M,ω) is guided by embedded J-holomorphic curves. Further, we prove that for any fixed sizes blowups, when the area ratio μ between the section and fiber goes to infinity, there is a topological colimit of Symp(M,ω_μ). Moreover, when the blowup sizes are all equal to half the area of the fiber class, we give a topological model of the colimit which induces non-trivial symplectic mapping classes in Symp(M,ω) ∩ \rm Diff₀(M), where \rm Diff₀(M) is the identity component of the diffeomorphism group. These mapping classes are not Dehn twists along Lagrangian spheres.

Related

• Symplectic isotopy on non-minimal ruled surfaces
• Symplectomorphism groups and almost complex structures
• Moment maps, symplectomorphism groups and compatible complex structures
• On symplectic stabilisations and mapping classes
• Symplectormophism groups of non-compact manifolds, orbifold balls, and a space of Lagrangians