Diffeomorphism of simply connected algebraic surfaces

Details Diffeomorphism of simply connected algebraic surfaces Diffeomorphism of simply connected algebraic surfaces

2004-05-14

arxiv.org/abs/math/0405299v2

Mathematics

Algebraic Geometry

33 pages, 9 figures. Revised version with irrelevant mistake removed (braid group of the sphere replaced by mapping class grou

Scientific paper

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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