Open Access
June 2007 Diffeomorphism of simply connected algebraic surfaces
Fabrizio Catanese, Bronislaw Wajnryb
J. Differential Geom. 76(2): 117-213 (June 2007). DOI: 10.4310/jdg/1180135677


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.


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Fabrizio Catanese. Bronislaw Wajnryb. "Diffeomorphism of simply connected algebraic surfaces." J. Differential Geom. 76 (2) 117 - 213, June 2007.


Published: June 2007
First available in Project Euclid: 25 May 2007

zbMATH: 1127.14039
MathSciNet: MR2330412
Digital Object Identifier: 10.4310/jdg/1180135677

Rights: Copyright © 2007 Lehigh University

Vol.76 • No. 2 • June 2007
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