Karoubi conjecture

The Karoubi conjecture is a hypothesis in the field of algebraic topology, particularly concerning the relationships between certain types of groups associated with topological spaces. Specifically, it relates to the K-theory of a space and the structure of its stable homotopy category. In more technical terms, the conjecture posits that every homotopy equivalence between simply-connected spaces induces an isomorphism on their stable homotopy categories.