In this paper we exhibit
smooth 2-manifolds F2 in the 4-sphere S4 having the property that the second
homology of the group π1(S4− F2) is nontrivial. In particular, we obtain tori for
which H2(π1)≅Z2 and, by forming connected sums, surfaces of genus n for which
H2(π1) is the direct sum of n copies of Z2. Corollaries include: (1) There are knotted
surfaces in S4 that cannot be constructed by forming connected sums of unknotted
surfaces and knotted 2-spheres. (2) The class of groups that occur as knot groups of
surfaces in S4 is not contained in the class of high dimensional knot groups of Sn in
Sn+2.