About: Property P conjecture

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In mathematics, the Property P conjecture is a statement about 3-manifolds obtained by Dehn surgery on a knot in the 3-sphere. A knot in the 3-sphere is said to have Property P if every 3-manifold obtained by performing (non-trivial) Dehn surgery on the knot is not simply-connected. The conjecture states that all knots, except the unknot, have Property P. Research on Property P was started by R. H. Bing, who popularized the name and conjecture. A proof was announced in 2004, as the combined result of efforts of mathematicians working in several different fields.

Attributes	Values
rdf:type	yago:WikicatConjectures yago:Abstraction100002137 yago:Cognition100023271 yago:Concept105835747 yago:Content105809192 yago:Hypothesis105888929 yago:Idea105833840 yago:PsychologicalFeature100023100 yago:Speculation105891783
rdfs:label	Eigenschaft P (de) Property P conjecture (en)
rdfs:comment	Eigenschaft P ist eine Eigenschaft von Knoten, die gemäß der 2004 von Peter Kronheimer und Tomasz Mrowka bewiesenen Property P conjecture allen nichttrivialen Knoten zukommt und die besagt, dass 1-Chirurgie am Knoten niemals eine ergibt. Diese Vermutung war von Bedeutung in der Entwicklung der 3-dimensionalen Topologie, insbesondere im Zusammenhang mit der Poincaré-Vermutung. (de) In mathematics, the Property P conjecture is a statement about 3-manifolds obtained by Dehn surgery on a knot in the 3-sphere. A knot in the 3-sphere is said to have Property P if every 3-manifold obtained by performing (non-trivial) Dehn surgery on the knot is not simply-connected. The conjecture states that all knots, except the unknot, have Property P. Research on Property P was started by R. H. Bing, who popularized the name and conjecture. A proof was announced in 2004, as the combined result of efforts of mathematicians working in several different fields. (en)
dcterms:subject	3-manifolds Conjectures that have been proved
Wikipage page ID	1294354 (xsd:integer)
Wikipage revision ID	1034649116 (xsd:integer)
Link from a Wikipage to another Wikipage	Berkeley, California Algebraic & Geometric Topology Dehn surgery Lickorish–Wallace theorem 3-manifolds Mathematics Geometry & Topology 3-sphere 3-manifold Knot group Conjectures that have been proved Poincaré conjecture Knot (mathematics) R. H. Bing Simply-connected dbr:Property_R_conjecture
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=naYJBAAAQBAJ%7Cmr=0515288
sameAs	Property P conjecture Property P conjecture Property P conjecture Property P conjecture Property P conjecture
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cite_book dbt:Cite_journal dbt:Short_description dbt:Inline-citations dbt:Topology-stub
has abstract	Eigenschaft P ist eine Eigenschaft von Knoten, die gemäß der 2004 von Peter Kronheimer und Tomasz Mrowka bewiesenen Property P conjecture allen nichttrivialen Knoten zukommt und die besagt, dass 1-Chirurgie am Knoten niemals eine ergibt. Diese Vermutung war von Bedeutung in der Entwicklung der 3-dimensionalen Topologie, insbesondere im Zusammenhang mit der Poincaré-Vermutung. (de) In mathematics, the Property P conjecture is a statement about 3-manifolds obtained by Dehn surgery on a knot in the 3-sphere. A knot in the 3-sphere is said to have Property P if every 3-manifold obtained by performing (non-trivial) Dehn surgery on the knot is not simply-connected. The conjecture states that all knots, except the unknot, have Property P. Research on Property P was started by R. H. Bing, who popularized the name and conjecture. This conjecture can be thought of as a first step to resolving the Poincaré conjecture, since the Lickorish–Wallace theorem says any closed, orientable 3-manifold results from Dehn surgery on a link.If a knot has Property P, then one cannot construct a counterexample to the Poincaré conjecture by surgery along . A proof was announced in 2004, as the combined result of efforts of mathematicians working in several different fields. (en)
gold:hypernym	Statement
prov:wasDerivedFrom	wikipedia-en:Property_P_conjecture?oldid=1034649116&ns=0
page length (characters) of wiki page	3189 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Property_P_conjecture
is Link from a Wikipage to another Wikipage of	Peter B. Kronheimer Geometry & Topology Contact geometry Tomasz Mrowka R. H. Bing
is foaf:primaryTopic of	wikipedia-en:Property_P_conjecture

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