K-theory
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English
Etymology
From circa 1960. The Template:M stands for Template:Der.
The theory developed out of algebraic geometry after the 1957 publication of work by German-born French mathematician Template:W.
Noun
- Template:Lb The study of rings R generated by the set of vector bundles over some topological space or scheme;
Template:Lb that part of algebraic topology comprising what is now called topological K-theory. - Template:Lb The cohomology generated by the set of vector bundles over some topological space or scheme.
Usage notes
- In mathematics:
- Following Template:W's 1957 publication of a proof of the Template:W, K-theory was developed as a subfield of algebraic topology (notably in relation to C*-algebra theory). This subfield is now known as Template:M.
- Subsequently, K-theory was generalised as a subfield of algebraic geometry, now often called Template:M.
- This development allows a revisionist definition of topological K-theory as "the application of tools from K-theory to problems in algebraic topology."
- In its current state, K-theory (in the area of study sense) comprises algebraic K-theory and topological K-theory.
- The term K-theory also refers (in its countable sense) to the cohomology (a ring whose multiplication operation is tensor product) that is the central subject of K-theory.
- Applications have also been found in:
- The study of operator algebras (within functional analysis), where K-theory is a fundamental tool.
- The study of certain kinds of invariant of large matrices.
- In physics:
- In condensed matter physics, K-theory is a tool used to classify certain materials of importance.
- In string theory, a variation called Template:M (aka K-theory with local coefficients) is the basis of an application called K-theory classification, by which certain (hypothetical) objects are classified.
Hyponyms
Derived terms
Translations
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