About: Topological K-theory

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In mathematics, topological K-theory is a branch of algebraic topology. It was founded to study vector bundles on topological spaces, by means of ideas now recognised as (general) K-theory that were introduced by Alexander Grothendieck. The early work on topological K-theory is due to Michael Atiyah and Friedrich Hirzebruch.

Attributes	Values
rdf:type	organisation
rdfs:label	Topologische K-Theorie (de) 위상 K이론 (ko) Topologische K-theorie (nl) Топологическая K-теория (ru) Topological K-theory (en) Topologisk K-teori (sv) Топологічна К-теорія (uk) 拓扑K-理论 (zh)
rdfs:comment	In der Mathematik, speziell in der algebraischen Topologie, beschäftigt sich die Topologische K-Theorie mit dem Studium von Vektorbündeln auf topologischen Räumen.Der Name K-Theorie wurde von Alexander Grothendieck kreiert; das K steht für „Klasse“ in einem sehr allgemeinen Sinn. (de) In mathematics, topological K-theory is a branch of algebraic topology. It was founded to study vector bundles on topological spaces, by means of ideas now recognised as (general) K-theory that were introduced by Alexander Grothendieck. The early work on topological K-theory is due to Michael Atiyah and Friedrich Hirzebruch. (en) 대수적 위상수학에서 위상 K이론(位相K理論, 영어: topological K-theory)은 위상 공간 위의 벡터 다발을 연구하는 분야이다. 보다 일반적인 K이론의 특수한 경우다. (ko) In de wiskunde, is topologische K-theorie een deelgebied van de algebraïsche topologie. Het werd ontwikkeld om vectorbundels op algemene topologische ruimten te bestuderen door middel van ideeën die nu erkend worden als (algemene) K-theorie, die werd geïntroduceerd door Alexander Grothendieck. Het vroege werk op het gebied van de topologische K-theorie is te danken aan Michael Atiyah en Friedrich Hirzebruch. (nl) В математике, топологическая K-теория является подразделом алгебраической топологии. В начале своего существования она применялась для изучения векторных расслоений на топологических пространствах с помощью идей, признанных в настоящее время частью (общей) K-теории, введенной Александром Гротендиком . Ранние работы по топологической K-теории принадлежат Майклу Атья и Фридриху Хирцебруху. (ru) Inom matematiken är topologisk K-teori en del av algebraisk topologi. Den skapades för att studera på topologiska rum med hjälp av tekniker som numera ses som (allmän) K-teori som introducerades av Alexander Grothendieck. Det tidiga arbetet med topologisk K-teori utfördes av Michael Atiyah och . (sv) В математиці, топологічна K-теорія є підрозділом алгебричної топології. На початку свого існування вона застосовувалася для вивчення векторних розшарувань на топологічних просторах за допомогою ідей алгебричної K-теорії, введеної Гротендіком. Ранні роботи по топологічній K-теорії належать Майклу Атія і Фрідріху Хірцебруху. (uk) 数学中，拓扑 K-理论（topological K-theory）是代数拓扑的一个分支。它是研究一般拓扑空间上向量丛时发现的，所用的是由亚历山大·格罗滕迪克引入的现在称为（一般）K-理论的想法。早期拓扑 K-理论的工作归于迈克尔·阿蒂亚与弗里德里希·希策布鲁赫。 (zh)
dcterms:subject	K-theory
Wikipage page ID	2912468 (xsd:integer)
Wikipage revision ID	1069731566 (xsd:integer)
Link from a Wikipage to another Wikipage	Algebraic K-theory Algebraic topology Atiyah-Hirzebruch spectral sequence C*-algebras Thom space Commutative monoid Compact space Mathematics Frank Adams Frequency Friedrich Hirzebruch Bott periodicity theorem Contractible space Operator K-theory Long exact sequence Short exact sequence Commutative ring Hopf invariant Splitting principle Suspension (topology) Adams operation K-theory Whitney sum Hausdorff space K-theory Pointed space Addison-Wesley Alexander Grothendieck Isomorphism class KK-theory KR-theory Atiyah–Hirzebruch spectral sequence Atiyah–Singer index theorem Riemann sphere Cohomology Homotopy category Tautological bundle Reduced homology Vector fields on spheres Contravariant functor Grothendieck group Michael Atiyah Raoul Bott Snaith's theorem Unitary group Vector bundle Space (mathematics) Ring homomorphism Springer-Verlag Steenrod operation Kernel of a homomorphism Chern character Natural homomorphism Colimit Coboundary Spectrum (homotopy theory) Trivial bundle Thom isomorphism theorem
Link from a Wikipage to an external page	http://www.math.cornell.edu/~hatcher/VBKT/VBpage.html https://www.researchgate.net/publication/330505308
sameAs	Topological K-theory Topological K-theory Topological K-theory Topological K-theory Topological K-theory Topological K-theory Topological K-theory Topological K-theory Topological K-theory Topological K-theory Topological K-theory
dbp:wikiPageUsesTemplate	dbt:Cite_arXiv dbt:Cite_book dbt:Cite_web dbt:Math dbt:Mvar dbt:Reflist dbt:Short_description
has abstract	In der Mathematik, speziell in der algebraischen Topologie, beschäftigt sich die Topologische K-Theorie mit dem Studium von Vektorbündeln auf topologischen Räumen.Der Name K-Theorie wurde von Alexander Grothendieck kreiert; das K steht für „Klasse“ in einem sehr allgemeinen Sinn. (de) In mathematics, topological K-theory is a branch of algebraic topology. It was founded to study vector bundles on topological spaces, by means of ideas now recognised as (general) K-theory that were introduced by Alexander Grothendieck. The early work on topological K-theory is due to Michael Atiyah and Friedrich Hirzebruch. (en)

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