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- Ganea_conjecture abstract "Ganea's conjecture is a claim in algebraic topology, now disproved. It states that where cat(X) 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, X and Y. Furthermore, cat(Sn)=1, for any sphere Sn, n>0. Thus, the conjecture amounts to cat(X × Sn) ≥ cat(X) + 1. 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 M and p a point in M. This work raises the question: For which spaces X is the Ganea condition, cat(X × Sn) = cat(X) + 1, satisfied? It has been conjectured that these are precisely the spaces X for which cat(X) equals a related invariant, Qcat(X).".
- Ganea_conjecture wikiPageID "8186879".
- Ganea_conjecture wikiPageRevisionID "440304580".
- Ganea_conjecture hasPhotoCollection Ganea_conjecture.
- Ganea_conjecture subject Category:Algebraic_topology.
- Ganea_conjecture subject Category:Disproved_conjectures.
- Ganea_conjecture type Abstraction100002137.
- Ganea_conjecture type Cognition100023271.
- Ganea_conjecture type Concept105835747.
- Ganea_conjecture type Content105809192.
- Ganea_conjecture type DisprovedConjectures.
- Ganea_conjecture type Hypothesis105888929.
- Ganea_conjecture type Idea105833840.
- Ganea_conjecture type PsychologicalFeature100023100.
- Ganea_conjecture type Speculation105891783.
- Ganea_conjecture comment "Ganea's conjecture is a claim in algebraic topology, now disproved. It states that where cat(X) 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, X and Y. Furthermore, cat(Sn)=1, for any sphere Sn, n>0. Thus, the conjecture amounts to cat(X × Sn) ≥ cat(X) + 1. The conjecture was formulated by Tudor Ganea in 1971.".
- Ganea_conjecture label "Ganea conjecture".
- Ganea_conjecture sameAs m.026vl3_.
- Ganea_conjecture sameAs Q5520800.
- Ganea_conjecture sameAs Q5520800.
- Ganea_conjecture sameAs Ganea_conjecture.
- Ganea_conjecture wasDerivedFrom Ganea_conjecture?oldid=440304580.
- Ganea_conjecture isPrimaryTopicOf Ganea_conjecture.