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In an area of mathematics called differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere. That is, M is a sphere from the point of view of all its topological properties, but carrying a smooth structure that is not the familiar one (hence the name "exotic").

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rdf:type	place yago:Artifact100021939 yago:Object100002684 yago:PhysicalEntity100001930 yago:YagoGeoEntity yago:YagoPermanentlyLocatedEntity yago:Structure104341686 yago:Whole100003553 yago:WikicatDifferentialStructures
rdfs:label	Exotic sphere (en) Sphère exotique (fr) 이국적 초구 모노이드 (ko) Exotische sfeer (nl) Экзотическая сфера (ru) Екзотична сфера (uk)
rdfs:comment	En mathématiques, et plus précisément en topologie différentielle, une sphère exotique est une variété différentielle M qui est homéomorphe, mais non difféomorphe, à la n-sphère euclidienne standard. Autrement dit, M est une sphère du point de vue de ses propriétés topologiques, mais sa structure différentielle (qui définit, par exemple, la notion de vecteur tangent) n'est pas la structure usuelle, d'où l'adjectif « exotique ». (fr) 미분위상수학에서 이국적 초구 모노이드(異國的超球monoid, 영어: monoid of exotic spheres)는 어떤 주어진 차원에서, 매끄러운 초구와 위상 동형이지만 미분 동형이 아닐 수 있는 매끄러운 유향 다양체들의 집합이다. 이 집합은 연결합을 통해 가환 모노이드를 이룬다. 4차원이 아닌 다른 모든 차원에서 이국적 초구 모노이드는 유한 아벨 군이지만, 4차원의 경우는 이 모노이드가 심지어 유한 집합인지 여부도 알려지지 않았다. (ko) Екзотична сфера — гладкий многовид М, що гомеоморфний, але не дифеоморфний стандартній n-сфері. (uk) Экзотическая сфера — гладкое многообразие М, которое гомеоморфно, но не диффеоморфно стандартной n-сфере. (ru) In an area of mathematics called differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere. That is, M is a sphere from the point of view of all its topological properties, but carrying a smooth structure that is not the familiar one (hence the name "exotic"). (en) In de differentiaaltopologie, een deelgebied van de wiskunde, is een exotische sfeer een differentieerbare variëteit die homeomorf is met de standaard euclidische -sfeer, maar niet daarmee diffeomorf. Dat betekent dat een dergelijke variëteit vanuit topologisch oogpunt weliswaar een sfeer is, maar vanuit het oogpunt van haar differentieerbare structuur juist geen sfeer is. Dus als dimensie heeft, bestaat er een homeomorfisme , maar is geen enkele een diffeomorfisme. (nl)
dcterms:subject	Surgery theory Differential structures Differential topology Spheres
Wikipage page ID	1114931 (xsd:integer)
Wikipage revision ID	1106870714 (xsd:integer)
Link from a Wikipage to another Wikipage	American Journal of Mathematics Quaternion Kervaire invariant problem Bernoulli number Derivative Algebraic & Geometric Topology Annals of Mathematics Homeomorphic Index of a subgroup J-homomorphism Continuous function Critical point (mathematics) Surgery theory Notices of the American Mathematical Society Smooth structure Edwin E. Moise Boundary (topology) Monoid N-sphere Connected sum Proceedings of the National Academy of Sciences Smooth function Stable homotopy groups of spheres Stephen Smale Differential structures Clutching construction Commentarii Mathematici Helvetici Complex manifold Kervaire invariant Tuple H-cobordism Differential topology Spheres Cyclic group Exotic R4 Exotic sphere Fiber bundle Diffeomorphism Differential topology Grigori Perelman Atlas (topology) Abelian group John Milnor Surgery theory Homeomorphism Homotopy sphere Jean Cerf Topology (journal) Diffeomorphic Differentiable manifold Bulletin de la Société Mathématique de France Piecewise linear manifold Poincaré conjecture Michael Freedman Orientability Cerf theory Surgery exact sequence List of unsolved problems in mathematics Finite group Moise's theorem Pseudoisotopy theorem Parallelizable manifold Seven-dimensional space Morse function Transactions of the American Mathematical Society Springer-Verlag Kirby–Siebenmann invariant Brieskorn sphere The Quarterly Journal of Mathematics Alexander Trick
Link from a Wikipage to an external page	http://www.nilesjohnson.net/seven-manifolds.html http://www.map.mpim-bonn.mpg.de/Gluck_construction%23References http://www.maths.ed.ac.uk/~aar/exotic.htm

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