Applications of braid group techniques to the decomposition of moduli spaces, new examples

Every smooth minimal complex algebraic surface of general type, X, may be mapped into a moduli space, Mc12(x), c2(x), of minimal surfaces of general type, all of which have the same Chern numbers. Using the braid group and braid monodromy, we construct infinitely many new examples of pairs of minimal surfaces of general type which have the same Chern numbers and nonisomorphic fundamental groups. Unlike previous examples, our results include X for which ¦π1(X)¦ is arbitrarily large. Moreover, the surfaces are of positive signature. This supports our goal of using the braid group and fundamental groups to decompose Mc12(x), c2(x) into connected components.