Novikov conjecture

The Novikov conjecture is a mathematical hypothesis about how certain geometric properties of shapes (or spaces) relate to algebraic features of their underlying structures. Specifically, it predicts that specific invariants—mathematical quantities associated with these spaces—remain unchanged under continuous deformations. These invariants connect geometry, topology, and algebra, and the conjecture suggests they are stable even when the shape is stretched or bent without tearing. While proven for many cases, it remains open in general, and its resolution would deepen our understanding of the relationship between a space's shape and its algebraic properties.