2022/02/14 by Olguta Buse, Olguţa Buşe, Jun Li +2
Mathematics · #Combinatorics #Computer science #Cone (formal languages) #Diffeomorphism #FOS: Mathematics #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Group (periodic table) #Holomorphic function #Mapping class group #Mathematical Dynamics and Fractals #Mathematics #Physics #Pure mathematics #Section (typography) #Surface (topology) #Symplectic Geometry (math.SG) #Symplectic geometry #Symplectomorphism #Topology (electrical circuits) #math.SG
paper · pdf · doi:10.48550/arxiv.2202.06795
published in arXiv (Cornell University) (Cornell University) · 25 pages. Comment welcome! arXiv admin note: text overlap with arXiv:2010.04616
arxiv created 2022/02/14 · openalex publication_date 2022/02/14 · arxiv updated 2022/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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,ωμ). 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.