Abstract
Let R be a commutative ring with an identity element. By an R-homology 3-sphere we will mean a closed oriented 3-manifold M such that H* (M, R) = H*(S3, R). In dimension three, the concepts of topological, smooth, and PL manifolds coincide, as do the concepts of diffeomorphism, homeomorphism and PL-homeomorphism, see [26] and [222]. Therefore, we can work in all three categories interchangeably. Usually, ℤ-homology spheres are referred to as integral homology spheres, and ℚ-homology spheres as rational homology spheres. Homology 3-spheres exist in abundance. We begin with some examples and constructions.