Connected components of moduli spaces (Q1090374)

Let S be a minimal surface of general type over the field of complex numbers and let M(S) be the coarse moduli space of complex structures on the oriented topological 4-manifold S. The following theorem shows that the number \(\lambda\) (S) of connected components of M(S) can be arbitrarily large: For each natural number k there exist minimal models \(S_ 1,...,S_ k\) of surfaces of general type such that \((a)\quad S_ i\) is simply connected \((i=1,...,k)\); \((b)\quad for\) \(i\neq j\), \(S_ i\) and \(S_ j\) are (orientedly) homeomorphic but not a deformation of each other.