Smooth structures on algebraic surfaces with finite fundamental group (Q753882)

The paper makes a contribution to the following conjecture: A smooth compact nonsingular algebraic surface with finite fundamental group has at least two smooth structures which are stable under blowing-ups. - The main result obtained is: Theorem. Let G be a finite group. Then there is a constant c(G) such that the conjecture holds for all algebraic surfaces X with \(\pi_ 1(X)\cong G\), Euler characteristic e(X)\(\geq c(G)\) and \(c^ 2_ 1(X)\geq 0.\) Corollary. Let G be a finite group. Then the conjecture is true for all but perhaps a finite number of homeomorphism types of minimal algebraic surfaces X with \(\pi_ 1(X)\cong G.\) Also a summary of the results (obtained by Donaldson, Freedman, Friedman- Morgan and others) concerning this conjecture is given.