Rational homology sphere

In algebraic topology, a rational homology ${\displaystyle n}$-sphere is an ${\displaystyle n}$-dimensional manifold with the same rational homology groups as the ${\displaystyle n}$-sphere. These serve, among other things, to understand which information the rational homology groups of a space can or cannot measure and which attenuations result from neglecting torsion in comparison to the (integral) homology groups of the space.