2004/05/14 by Fabrizio Catanese, Catanese, Fabrizio, Bronisław Wajnryb +2 · 1 citation
Mathematics · #14D05 #14J15 #14J29 #14J80 #57R50 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG) #math.AG #math.SG #msc:14D05 #msc:14J15 #msc:14J29 #msc:14J80 #msc:57R50
paper · pdf · doi:10.48550/arxiv.math/0405299
33 pages, 9 figures. Revised version with irrelevant mistake removed (braid group of the sphere replaced by mapping class group of the punctured sphere)
openalex publication_date 2004/05/14 · arxiv created 2005/07/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we show that even in the case of simply connected minimal algebraic surfaces of general type, deformation and differentiable equivalence do not coincide. Exhibiting several simple families of surfaces which are not deformation equivalent, and proving their diffeomorphism, we give a counterexample to a weaker form of the speculation DEF = DIFF of R. Friedman and J. Morgan, i.e., in the case where (by M. Freedman's theorem) the topological type is completely determined by the numerical invariants of the surface. We hope that the methods of proof may turn out to be quite useful to show diffeomorphism and indeed symplectic equivalence for many important classes of algebraic surfaces and symplectic 4-manifolds.