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The Novikov conjecture is one of the most important unsolved problems in topology. It is named for Sergei Novikov who originally posed the conjecture in 1965. The Novikov conjecture concerns the homotopy invariance of certain polynomials in the Pontryagin classes of a manifold, arising from the fundamental group. According to the Novikov conjecture, the higher signatures, which are certain numerical invariants of smooth manifolds, are homotopy invariants.

Attributes	Values
rdf:type	yago:WikicatConjectures yago:Abstraction100002137 yago:Cognition100023271 yago:Concept105835747 yago:Content105809192 yago:Hypothesis105888929 yago:Idea105833840 yago:PsychologicalFeature100023100 yago:Speculation105891783
rdfs:label	Novikov-Vermutung (de) Novikov conjecture (en)
rdfs:comment	In der Mathematik ist die Novikov-Vermutung eine für zahlreiche Gruppen bewiesene, aber im Allgemeinen offene Vermutung über die Topologie differenzierbarer Mannigfaltigkeiten mit Fundamentalgruppe . Sie hat zahlreiche Anwendungen in der Chirurgietheorie bei der Klassifikation der Differentialstrukturen zu einem gegebenen Homotopietyp. Sie würde aus der oder auch der folgen. (de) The Novikov conjecture is one of the most important unsolved problems in topology. It is named for Sergei Novikov who originally posed the conjecture in 1965. The Novikov conjecture concerns the homotopy invariance of certain polynomials in the Pontryagin classes of a manifold, arising from the fundamental group. According to the Novikov conjecture, the higher signatures, which are certain numerical invariants of smooth manifolds, are homotopy invariants. (en)
dcterms:subject	Conjectures Surgery theory Geometric topology Homotopy theory Unsolved problems in geometry
Wikipage page ID	3035194 (xsd:integer)
Wikipage revision ID	1119032535 (xsd:integer)
Link from a Wikipage to another Wikipage	Princeton University Press Homotopy equivalence L-theory Conjectures Surgery theory Classifying space Fundamental class Fundamental group Topology Pontryagin class Discrete group Geometric topology Homotopy theory Counterexample Jim Stasheff Abelian group Unsolved problems in geometry John Milnor Eilenberg–MacLane space Homotopy Assembly map Manifold Borel conjecture Polynomial Sergei Novikov (mathematician) Hirzebruch polynomial
Link from a Wikipage to an external page	http://www.map.him.uni-bonn.de/Novikov_Conjecture http://www.indiana.edu/~jfdavis/papers/d_manc.pdf http://www.scholarpedia.org/article/Novikov_conjecture https://www.math.umd.edu/~jmr/NC.html http://www.math.uni-muenster.de/u/lueck/publ/lueck/owsemfinalextract.pdf http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Novikov_Sergi.html http://www.maths.ed.ac.uk/~aar/books/novikov1.pdf http://www.maths.ed.ac.uk/~aar/books/novikov2.pdf
sameAs	Novikov conjecture Novikov conjecture Novikov conjecture Novikov conjecture Novikov conjecture
dbp:wikiPageUsesTemplate	dbt:About dbt:Citation
has abstract	In der Mathematik ist die Novikov-Vermutung eine für zahlreiche Gruppen bewiesene, aber im Allgemeinen offene Vermutung über die Topologie differenzierbarer Mannigfaltigkeiten mit Fundamentalgruppe . Sie hat zahlreiche Anwendungen in der Chirurgietheorie bei der Klassifikation der Differentialstrukturen zu einem gegebenen Homotopietyp. Sie macht eine Aussage über die Homotopieinvarianz gewisser Kombinationen rationaler Pontrjagin-Klassen. Rationale Pontrjaginklassen sind Invarianten differenzierbarer Mannigfaltigkeiten, die nach einem Satz von Novikov invariant unter Homöomorphismen, aber im Allgemeinen nicht invariant unter Homotopieäquivalenzen sind. Für die aus den Pontrjaginklassen gebildete L-Klasse ist nach dem Signatursatz von Hirzebruch die homotopieinvariante Signatur. Die Novikov-Vermutung gibt (in Abhängigkeit von der Fundamentalgruppe) weitere homotopieinvariante Kombinationen. Es wird vermutet, dass sich alle homotopieinvarianten Kombinationen rationaler Pontrjaginklassen aus den in der Novikov-Vermutung betrachteten höheren Signaturen ergeben. Sie würde aus der oder auch der folgen. (de) The Novikov conjecture is one of the most important unsolved problems in topology. It is named for Sergei Novikov who originally posed the conjecture in 1965. The Novikov conjecture concerns the homotopy invariance of certain polynomials in the Pontryagin classes of a manifold, arising from the fundamental group. According to the Novikov conjecture, the higher signatures, which are certain numerical invariants of smooth manifolds, are homotopy invariants. The conjecture has been proved for finitely generated abelian groups. It is not yet known whether the Novikov conjecture holds true for all groups. There are no known counterexamples to the conjecture. (en)
prov:wasDerivedFrom	wikipedia-en:Novikov_conjecture?oldid=1119032535&ns=0
page length (characters) of wiki page	4787 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Novikov_conjecture
is Link from a Wikipage to another Wikipage of	Scalar curvature List of Vanderbilt University people List of conjectures Algebraic K-theory John Roe (mathematician) L-theory Geometric group theory Novikov Baum–Connes conjecture Henri Moscovici Haagerup property Farrell–Jones conjecture List of Russian mathematicians List of Russian scientists Gunnar Carlsson Asymptotic dimension Borel conjecture Sergei Novikov (mathematician) Guoliang Yu List of unsolved problems in mathematics Small cancellation theory List of Russian people Wu-Chung Hsiang
is Wikipage disambiguates of	Novikov
is known for of	Sergei Novikov (mathematician)
is known for of	Sergei Novikov (mathematician)
is foaf:primaryTopic of	wikipedia-en:Novikov_conjecture

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