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- Ganea's conjecture is a claim in algebraic topology, now disproved. It states that for all , where is the Lusternik–Schnirelmann category of a topological space X, and Sn is the n-dimensional sphere. The inequality holds for any pair of spaces, and . Furthermore, , for any sphere , . Thus, the conjecture amounts to . The conjecture was formulated by Tudor Ganea in 1971. Many particular cases of this conjecture were proved, till finally Norio Iwase gave a counterexample in 1998. In a follow-up paper from 2002, Iwase gave an even stronger counterexample, with X a closed, smooth manifold. This counterexample also disproved a related conjecture, stating that for a closed manifold and a point in . A minimum dimensional counterexample to Ganea’s conjecture was constructed by Don Stanley and Hugo Rodríguez Ordóñez in 2010. This work raises the question: For which spaces X is the Ganea condition, , satisfied? It has been conjectured that these are precisely the spaces X for which equals a related invariant, (en)
- 가네아 추측(Ganea's conjecture)은 대수적 위상수학의 명제 중 하나로, 반례가 발견되어 거짓임이 밝혀졌다. (ko)
- Inom matematiken är Ganeas förmodan en numera motbevisad förmodan som säger att där cat(X) är av ett topologiskt rum X och Sn är n-dimensionella sfären. Den formulerades av år 1971. (sv)
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- 가네아 추측(Ganea's conjecture)은 대수적 위상수학의 명제 중 하나로, 반례가 발견되어 거짓임이 밝혀졌다. (ko)
- Inom matematiken är Ganeas förmodan en numera motbevisad förmodan som säger att där cat(X) är av ett topologiskt rum X och Sn är n-dimensionella sfären. Den formulerades av år 1971. (sv)
- Ganea's conjecture is a claim in algebraic topology, now disproved. It states that for all , where is the Lusternik–Schnirelmann category of a topological space X, and Sn is the n-dimensional sphere. The inequality holds for any pair of spaces, and . Furthermore, , for any sphere , . Thus, the conjecture amounts to . for a closed manifold and a point in . A minimum dimensional counterexample to Ganea’s conjecture was constructed by Don Stanley and Hugo Rodríguez Ordóñez in 2010. (en)
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- Ganea conjecture (en)
- 가네아 추측 (ko)
- Ganeas förmodan (sv)
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