Every simply-connected rational homology sphere is, in fact, the usual sphere in dimensions $2, 3.$ Is this true in dimension 4? Where are the first counterexamples? (I know there are some in dimension 7.) Yes, a topological category is fine, to avoid the smooth Poincare conjecture.

Every simply-connected rational homology sphere is, in fact, the usual sphere in dimensions $2, 3.$ Is this true in dimension 4? Where are the first counterexamples? (I know there are some in dimension 7.) Yes, the topological category is fine, to avoid the smooth Poincaré conjecture.

Every simply connected rational homology sphere is, in fact, the usual sphere in dimensions $2, 3.$ Is this true in dimension 4? Where are the first counterexamples? (I know there are some in dimension 7). Yes, topological category is fine, to avoid the smooth Poincare conjecture.

Every simply-connected rational homology sphere is, in fact, the usual sphere in dimensions $2, 3.$ Is this true in dimension 4? Where are the first counterexamples? (I know there are some in dimension 7.) Yes, a topological category is fine, to avoid the smooth Poincare conjecture.