“Group actions on surfaces of general type”
Ron Stern, University of California at Irvine

Abstract:
The automorphism group of an algebraic surfaces of general type is known to be finite. Since a diffeomorphism of such a surface, when viewed as a smooth 4-manifold, must preserve the Seiberg-Witten and Donaldson basic classes, one would suspect that the diffeomorphism group of a surface of general type demonstrate some finiteness properties. For example: Are there only finitely many smoothly distinct but topologically equivalent smooth actions of a fixed cyclic group? We will report on joint work with Ron Fintushel and Nathan Sunukjian that many surfaces of general type have, in fact, infinitely many distinct smooth but topologically equivalent actions of a fixed cyclic group.