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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. , this statement is still commonly referred to as the Segal conjecture, even though it now has the status of a theorem. ==Statement of the 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 : Here, lim denotes the inverse limit, πS * denotes the stable cohomotopy ring, ''B'' denotes the classifying space, the superscript ''k'' denotes the ''k''-skeleton, and the subscript + denotes the addition of a disjoint basepoint. On the right-hand side, the hat denotes the completion of the Burnside ring with respect to its augmentation ideal. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Segal conjecture」の詳細全文を読む スポンサード リンク
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