2001/10/29 by Olguta Buse, Olguţa Buşe, Buse, Olguta
Mathematics · #14B07 #53C15 #53D45 #57R17 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.AG #math.DG #math.SG #msc:14B07 #msc:53C15 #msc:53D45 #msc:57R17
paper · pdf · doi:10.48550/arxiv.math/0110313
23 pages
arxiv created 2001/10/29 · openalex publication_date 2001/10/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the symplectomorphism groups Gλ=Symp0(M,ωλ) of an arbitrary closed manifold M equipped with a 1-parameter family of symplectic forms ωλ with variable cohomology class. We show that the existence of nontrivial elements in π_*(\cal A,\cal A'), where (\cal A,\cal A') is a suitable pair of spaces of almost complex structures, implies the exiarxiv.org stence of families of nontrivial elements in π*-iGλ, for i=1 or 2. Suitable parametric Gromov Witten invariants detect nontrivial elements in π_*(\cal A,\cal A'). By looking at certain resolutions of quotient singularities we investigate the situation (M,ωλ)= (S2 × S2 × X,σF ⊕ λσB ⊕ ωst), with (X,ωst) an arbitrary symplectic manifold. We find families of nontrivial elements in πk(GλX), for countably many k and different values of λ. In particular we show that the fragile elements wℓ found by Abreu-McDuff in π4 ℓ(Gℓ+1pt) do not disappear when we consider them in S2 × S2 × X.