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In mathematics, the fundamental class is a homology class [M] associated to a connected orientable compact manifold of dimension n, which corresponds to the generator of the homology group . The fundamental class can be thought of as the orientation of the top-dimensional simplices of a suitable triangulation of the manifold.

Attributes	Values
rdfs:label	Fundamentalklasse (de) Fundamental class (en) 기본류 (ko) 基本類 (ja) Фундаментальный класс (ru)
rdfs:comment	In der Mathematik bezeichnet man als Fundamentalklasse einen Erzeuger der höchsten Homologiegruppe einer Mannigfaltigkeit. Im Falle triangulierter Mannigfaltigkeiten kann man die Fundamentalklasse durch die formale Summe der kohärent orientierten Simplizes der Triangulierung repräsentieren. Zykel, welche die Fundamentalklasse repräsentieren (d. h., deren Homologieklasse die Fundamentalklasse ist), werden als Fundamentalzykel bezeichnet. (de) In mathematics, the fundamental class is a homology class [M] associated to a connected orientable compact manifold of dimension n, which corresponds to the generator of the homology group . The fundamental class can be thought of as the orientation of the top-dimensional simplices of a suitable triangulation of the manifold. (en) 数学において、基本類(fundamental class)は、向きづけられた多様体 M に付随するホモロジー類 [M] であり、ホモロジー群の生成子に対応する。基本類は、多様体の適切な三角分割の最高次数の単体の向きと考えることができる。 (ja) 대수적 위상수학에서 기본류(基本類, 영어: fundamental class)는 다양체 전체에 해당하는 호몰로지 동치류이다. (ko) Фундаментальным классом называется гомологический класс ориентированного многообразия, который соответствует «целому многообразию». Интуитивно фундаментальный класс можно себе представить как сумму симплексов максимальной размерности подходящей триангуляции многообразия. Фундаментальный класс многообразия обычно обозначается . (ru)
dcterms:subject	Algebraic topology
Wikipage page ID	669440 (xsd:integer)
Wikipage revision ID	1025060289 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press De Rham cohomology Lie group Stiefel–Whitney class Mathematics Connected space Simplex Closed manifold Poincaré duality Algebraic topology Homology (mathematics) Twisted Poincaré duality Differential form Schubert cell Infinite cyclic Bruhat decomposition Longest element of a Coxeter group Orientable Flag variety
Link from a Wikipage to an external page	https://www.math.cornell.edu/~hatcher/AT/ATpage.html%7Ctitle=Algebraic http://www.map.mpim-bonn.mpg.de/Fundamental_class http://www.encyclopediaofmath.org/index.php/Fundamental_class
sameAs	Fundamental class Fundamental class Fundamental class Fundamental class Fundamental class Fundamental class Fundamental class
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Expand_section dbt:For dbt:Main dbt:Unreferenced
has abstract	In der Mathematik bezeichnet man als Fundamentalklasse einen Erzeuger der höchsten Homologiegruppe einer Mannigfaltigkeit. Im Falle triangulierter Mannigfaltigkeiten kann man die Fundamentalklasse durch die formale Summe der kohärent orientierten Simplizes der Triangulierung repräsentieren. Zykel, welche die Fundamentalklasse repräsentieren (d. h., deren Homologieklasse die Fundamentalklasse ist), werden als Fundamentalzykel bezeichnet. (de) In mathematics, the fundamental class is a homology class [M] associated to a connected orientable compact manifold of dimension n, which corresponds to the generator of the homology group . The fundamental class can be thought of as the orientation of the top-dimensional simplices of a suitable triangulation of the manifold. (en) 数学において、基本類(fundamental class)は、向きづけられた多様体 M に付随するホモロジー類 [M] であり、ホモロジー群の生成子に対応する。基本類は、多様体の適切な三角分割の最高次数の単体の向きと考えることができる。 (ja) 대수적 위상수학에서 기본류(基本類, 영어: fundamental class)는 다양체 전체에 해당하는 호몰로지 동치류이다. (ko) Фундаментальным классом называется гомологический класс ориентированного многообразия, который соответствует «целому многообразию». Интуитивно фундаментальный класс можно себе представить как сумму симплексов максимальной размерности подходящей триангуляции многообразия. Фундаментальный класс многообразия обычно обозначается . (ru)
prov:wasDerivedFrom	wikipedia-en:Fundamental_class?oldid=1025060289&ns=0
page length (characters) of wiki page	3910 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Fundamental_class
is Link from a Wikipage to another Wikipage of	List of algebraic topology topics Hodge conjecture Characteristic class De Rham invariant Degree of a continuous mapping Donaldson–Thomas theory Kuranishi structure Stiefel–Whitney class Essential manifold Gauge theory (mathematics) Generalized flag variety Genus of a multiplicative sequence Novikov conjecture Timeline of bordism Timeline of manifolds Pontryagin class Poincaré duality Glossary of symplectic geometry Hirzebruch signature theorem Hirzebruch–Riemann–Roch theorem Lefschetz duality Gromov's systolic inequality for essential manifolds Intersection theory Chern class Systolic geometry Cobordism Cohomology Eilenberg–MacLane space Twisted Poincaré duality Differential form Borel–Moore homology Classifying space for U(n) Filling radius Gromov–Witten invariant Bruhat decomposition Longest element of a Coxeter group Euler characteristic Euler class Gysin homomorphism Immersion (mathematics) Poincaré space Simplicial volume Weil group Orientation homology class Fundamental homology class

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