About: Spectrum (topology)

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In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. Every such cohomology theory is representable, as follows from Brown's representability theorem. This means that, given a cohomology theory , there exist spaces such that evaluating the cohomology theory in degree on a space is equivalent to computing the homotopy classes of maps to the space , that is .

Attributes	Values
rdf:type	Thing
rdfs:label	Spektrum (Topologie) (de) Spectre (topologie) (fr) 스펙트럼 (위상수학) (ko) Spectrum (topology) (en)
rdfs:comment	Im mathematischen Teilgebiet der algebraischen Topologie werden Spektren zur Definition verallgemeinerter Homologietheorien benutzt. (de) 호모토피 이론에서 스펙트럼(영어: spectrum)은 을 나타내는 위상수학적 구조이다. 서로 특정 연속 함수들로 연결된 점을 가진 공간들의 열로서 표현될 수 있다. (ko) En topologie algébrique, une branche des mathématiques, un spectre est un objet représentant une théorie cohomologique généralisée (qui découle du (en)). Cela signifie que, étant donné une théorie de cohomologie , il existe des espaces tels que l'évaluation de la théorie cohomologique en degré sur un espace équivaut à calculer les classes d'homotopie des morphismes à l'espace , soit encore . (fr) In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. Every such cohomology theory is representable, as follows from Brown's representability theorem. This means that, given a cohomology theory , there exist spaces such that evaluating the cohomology theory in degree on a space is equivalent to computing the homotopy classes of maps to the space , that is . (en)
rdfs:seeAlso	Generalized cohomology theory
dcterms:subject	Homotopy theory
Wikipage page ID	1033697 (xsd:integer)
Wikipage revision ID	1124275620 (xsd:integer)
Link from a Wikipage to another Wikipage	List of cohomology theories Monoidal category Proceedings of the London Mathematical Society Algebraic topology Derived algebraic geometry Derived tensor product 0-sphere Mathematics Classifying space Edwin Spanier Elon Lages Lima Frank Adams George W. Whitehead Monoid Connective spectrum Freudenthal suspension theorem Suspension (topology) Topological Hochschild homology Mapping cone (topology) Mapping spectrum Mathematical Proceedings of the Cambridge Philosophical Society Adams spectral sequence Triangulated category G-spectrum K-theory spectrum Allen Hatcher Brown's representability theorem Smash product Homotopy theory Topological K-theory Abelian group Cohomology Eilenberg–MacLane space Homotopy category Module spectrum Sphere spectrum CW complex Grothendieck group Michael Atiyah Michael Boardman Category (mathematics) Unitary group University of Chicago Press Symmetric spectrum Representable functor Ring spectrum Transactions of the American Mathematical Society Spectral geometry Bott periodicity Ring axioms E-infinity ring spectrum Vector bundles dbr:Rainer_Vogt Whitehead tower Simplicial spectrum Singular cohomology Infinite loop space Stable homotopy group Thom spectrum dbr:Periodic_spectrum
Link from a Wikipage to an external page	https://mathoverflow.net/q/117684 https://books.google.com/books%3Fid=xlvvAAAAMAAJ http://pi.math.cornell.edu/~hatcher/AT/ATch5.pdf http://www.math.uchicago.edu/~may/PAPERS/Newfirst.pdf https://books.google.com/books%3Fid=6vG13YQcPnYC http://www.math.uni-bonn.de/~schwede/SymSpec.pdf
sameAs	Spectrum (topology) Spectrum (topology) Spectrum (topology) Spectrum (topology) Spectrum (topology) Spectrum (topology)
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cite_book dbt:Cite_journal dbt:Cite_web dbt:Main dbt:Main_articles dbt:Reflist dbt:See_also
has abstract	Im mathematischen Teilgebiet der algebraischen Topologie werden Spektren zur Definition verallgemeinerter Homologietheorien benutzt. (de) En topologie algébrique, une branche des mathématiques, un spectre est un objet représentant une théorie cohomologique généralisée (qui découle du (en)). Cela signifie que, étant donné une théorie de cohomologie , il existe des espaces tels que l'évaluation de la théorie cohomologique en degré sur un espace équivaut à calculer les classes d'homotopie des morphismes à l'espace , soit encore . Remarquons qu'il existe plusieurs catégories de spectres différentes conduisant à de nombreuses difficultés techniques, mais ils déterminent tous la même (en), connue sous le nom de catégorie d'homotopie stable. C'est l'un des points clés de l'introduction des spectres car ils forment un foyer naturel pour la théorie de l'homotopie stable. (fr) In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. Every such cohomology theory is representable, as follows from Brown's representability theorem. This means that, given a cohomology theory , there exist spaces such that evaluating the cohomology theory in degree on a space is equivalent to computing the homotopy classes of maps to the space , that is . Note there are several different categories of spectra leading to many technical difficulties, but they all determine the same homotopy category, known as the stable homotopy category. This is one of the key points for introducing spectra because they form a natural home for stable homotopy theory. (en) 호모토피 이론에서 스펙트럼(영어: spectrum)은 을 나타내는 위상수학적 구조이다. 서로 특정 연속 함수들로 연결된 점을 가진 공간들의 열로서 표현될 수 있다. (ko)
prov:wasDerivedFrom	wikipedia-en:Spectrum_(topology)?oldid=1124275620&ns=0
page length (characters) of wiki page	21637 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Spectrum_(topology)

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