claim: Scandinavia does not include the remote Norwegian islands of Svalbard and Jan Mayen as of 2002.
evidence: In algebraic topology , a Poincare space is an n-dimensional topological space with a distinguished element µ of its nth homology group such that taking the cap product with an element of the kth cohomology group yields an isomorphism to the -LRB- n − k -RRB- th homology group .. algebraic topology. algebraic topology. topological space. topological space. homology group. homology group. cap product. cap product. cohomology. cohomology. The space is essentially one for which Poincare duality is valid ; more precisely , one whose singular chain complex forms a Poincare complex with respect to the distinguished element µ .. Poincare duality. Poincare duality. Poincare complex. Poincare complex. For example , any closed , orientable , connected manifold M is a Poincare space , where the distinguished element is the fundamental class. fundamental class. fundamental class. Poincare spaces are used in surgery theory to analyze and classify manifolds .. surgery theory. surgery theory. Not every Poincare space is a manifold , but the difference can be studied , first by having a normal map from a manifold , and then via obstruction theory .. normal map. Normal invariant. obstruction theory. obstruction theory