High Quality Content by WIKIPEDIA articles! Segal's Burnside ring conjecture, or, more briefly, the Segal conjecture, is a theorem in homotopy theory, a branch of mathematics. The theorem relates the Burnside ring of a finite group G to the stable cohomotopy of the classifying space BG. The conjecture was made by Graeme Segal and proved by Gunnar Carlsson. As of 2006[update], this statement is still commonly referred to as the Segal conjecture, even though it now has the status of a theorem.The Segal conjecture has several different formulations, not all of which are equivalent. Here is a weak form: there exists, for every finite group G, an isomorphism