About: Arithmetic hyperbolic 3-manifold

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In mathematics, more precisely in group theory and hyperbolic geometry, Arithmetic Kleinian groups are a special class of Kleinian groups constructed using orders in quaternion algebras. They are particular instances of arithmetic groups. An arithmetic hyperbolic three-manifold is the quotient of hyperbolic space by an arithmetic Kleinian group.

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rdfs:label	Arithmetic hyperbolic 3-manifold (en) 数論的双曲3次元多様体 (ja)
rdfs:comment	In mathematics, more precisely in group theory and hyperbolic geometry, Arithmetic Kleinian groups are a special class of Kleinian groups constructed using orders in quaternion algebras. They are particular instances of arithmetic groups. An arithmetic hyperbolic three-manifold is the quotient of hyperbolic space by an arithmetic Kleinian group. (en) 数学において、数論的双曲3次元多様体（英: arithmetic hyperbolic 3-manifold）は、双曲3次元多様体であって、その基本群がの部分群としてであるような多様体である。これらの中で最も小さな体積の多様体は、ウィークス多様体であり、次に小さな体積の多様体はである。 (ja)
dcterms:subject	3-manifolds Kleinian groups Riemannian manifolds Number theory Hyperbolic geometry
Wikipage page ID	15239331 (xsd:integer)
Wikipage revision ID	1091258774 (xsd:integer)
Link from a Wikipage to another Wikipage	Meyerhoff manifold Bianchi group Ring of integers Dedekind zeta function 3-manifolds Kleinian groups Mathematics Weeks manifold Riemannian manifolds Order (ring theory) Arithmetic group Commensurability (group theory) Trace field William Thurston Haar measure Lattice (discrete subgroup) Algebraic integer Number theory Extension of scalars Figure-eight knot (mathematics) Hyperbolic geometry Number field Central simple algebra Hyperbolic Dehn surgery Hyperbolic geometry Hyperbolic space Discriminant Group theory Ian Agol Kleinian group Quaternion algebra Virtually Haken conjecture Hamilton quaternions Springer-Verlag Ramanujan conjecture Imaginary quadratic field
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=yrmT56mpw3kC
sameAs	Arithmetic hyperbolic 3-manifold Arithmetic hyperbolic 3-manifold Arithmetic hyperbolic 3-manifold Arithmetic hyperbolic 3-manifold Arithmetic hyperbolic 3-manifold
dbp:wikiPageUsesTemplate	dbt:Block_indent dbt:Citation dbt:Main dbt:Reflist dbt:Sfn
em	1.500000 (xsd:double)
text	Given there are at most finitely many arithmetic hyperbolic 3–manifolds with volume less than . (en)
has abstract	In mathematics, more precisely in group theory and hyperbolic geometry, Arithmetic Kleinian groups are a special class of Kleinian groups constructed using orders in quaternion algebras. They are particular instances of arithmetic groups. An arithmetic hyperbolic three-manifold is the quotient of hyperbolic space by an arithmetic Kleinian group. (en) 数学において、数論的双曲3次元多様体（英: arithmetic hyperbolic 3-manifold）は、双曲3次元多様体であって、その基本群がの部分群としてであるような多様体である。これらの中で最も小さな体積の多様体は、ウィークス多様体であり、次に小さな体積の多様体はである。 (ja)
gold:hypernym	Manifold
prov:wasDerivedFrom	wikipedia-en:Arithmetic_hyperbolic_3-manifold?oldid=1091258774&ns=0
page length (characters) of wiki page	11966 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Arithmetic_hyperbolic_3-manifold
is Link from a Wikipage to another Wikipage of	Meyerhoff manifold Weeks manifold Arithmetic group Alan Reid (mathematician) Algebraic number theory Don Zagier Arithmetic Kleinian group
is Wikipage redirect of	Arithmetic Kleinian group
is foaf:primaryTopic of	wikipedia-en:Arithmetic_hyperbolic_3-manifold

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