Deformation, differentiable and
symplectic equivalence for algebraic surfaces
Bayreuth, Germany
Abstract
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In the talk I will report about joint work with B. Wajnryb. First on the results which we already obtained, showing that even in the case of simply connected minimal algebraic surfaces of general type, deformation and differentiable equivalence do not coincide. Exhibiting the simple families of abc surfaces
which are not deformation equivalent, and proving their diffeomorphism, we get 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. The methods of proof are rather general, but if we want
to investigate the natural symplectic structures associated to the canonical
class, the question of symplectic equivalence becomes more subtle in the 1-connected case. I will explain also work in progress on this second question, especially some beautiful geometry of discriminant curves. |