Novikov conjecture

The Novikov conjecture is a significant hypothesis in the field of topology and geometry, particularly concerning the relationships between the algebraic topology of manifolds and their geometric structure. It was proposed by the Russian mathematician Sergei Novikov in the 1970s. At its core, the Novikov conjecture deals with the higher dimensional homotopy theory, specifically the relationship between the homotopy type of a manifold and the groups of self-homotopy equivalences of the manifold.