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In the branch of mathematics called knot theory, the volume conjecture is the following open problem that relates quantum invariants of knots to the hyperbolic geometry of knot complements. Let O denote the unknot. For any knot K let be Kashaev's invariant of ; this invariant coincides with the following evaluation of the -Colored Jones Polynomial of : Then the volume conjecture states that where vol(K) denotes the hyperbolic volume of the complement of K in the 3-sphere.

Attributes	Values
rdfs:label	体積予想 (ja) Volume conjecture (en)
rdfs:comment	結び目理論という数学の分野では、体積予想(volume conjecture)は、次のように結び目の量子不変量と結び目補空間の双曲幾何学とを関係付ける予想である。 O で自明な結び目を表すとする。任意の結び目 K に対し、でのカシャエフ(Kashaev)不変量を表す。カシャエフの不変量は、の -色付きジョーンズ多項式の評価式 (1) と一致する。体積予想は、 (2) という予想である。ここに、vol(K) は 3次元球面の中の K の補空間の双曲体積である。 (ja) In the branch of mathematics called knot theory, the volume conjecture is the following open problem that relates quantum invariants of knots to the hyperbolic geometry of knot complements. Let O denote the unknot. For any knot K let be Kashaev's invariant of ; this invariant coincides with the following evaluation of the -Colored Jones Polynomial of : Then the volume conjecture states that where vol(K) denotes the hyperbolic volume of the complement of K in the 3-sphere. (en)
dcterms:subject	Conjectures Knot theory Unsolved problems in geometry
Wikipage page ID	22173048 (xsd:integer)
Wikipage revision ID	1097962345 (xsd:integer)
Link from a Wikipage to another Wikipage	Conjectures Mathematics Chern–Simons theory R-matrix Quantum invariant Acta Mathematica Jones polynomial 3-sphere Figure-eight knot Knot complement Knot theory Knot theory Hyperbolic geometry Hyperbolic knot Hyperbolic volume Unsolved problems in geometry Discrete Fourier transform Stevedore knot (mathematics) Quantum dilogarithm Unknot Three-twist knot Vassiliev invariant Trivial knot
sameAs	Volume conjecture Volume conjecture Volume conjecture Volume conjecture
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harvtxt dbt:NumBlk dbt:Short_description dbt:EquationRef dbt:Harvs
has abstract	結び目理論という数学の分野では、体積予想(volume conjecture)は、次のように結び目の量子不変量と結び目補空間の双曲幾何学とを関係付ける予想である。 O で自明な結び目を表すとする。任意の結び目 K に対し、でのカシャエフ(Kashaev)不変量を表す。カシャエフの不変量は、の -色付きジョーンズ多項式の評価式 (1) と一致する。体積予想は、 (2) という予想である。ここに、vol(K) は 3次元球面の中の K の補空間の双曲体積である。 (ja) In the branch of mathematics called knot theory, the volume conjecture is the following open problem that relates quantum invariants of knots to the hyperbolic geometry of knot complements. Let O denote the unknot. For any knot K let be Kashaev's invariant of ; this invariant coincides with the following evaluation of the -Colored Jones Polynomial of : Then the volume conjecture states that where vol(K) denotes the hyperbolic volume of the complement of K in the 3-sphere. (en)
prov:wasDerivedFrom	wikipedia-en:Volume_conjecture?oldid=1097962345&ns=0
page length (characters) of wiki page	4377 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Volume_conjecture
is Link from a Wikipage to another Wikipage of	List of knot theory topics Quantum invariant Jones polynomial List of unsolved problems in mathematics
is foaf:primaryTopic of	wikipedia-en:Volume_conjecture

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