K-theory

Etymology
From circa 1960. The stands for.

The theory developed out of algebraic geometry after the 1957 publication of work by German-born French mathematician.

Noun

 * 1)  The study of rings R generated by the set of vector bundles over some topological space or scheme;  that part of algebraic topology comprising what is now called topological K-theory.
 * 2)  The cohomology generated by the set of vector bundles over some topological space or scheme.
 * 1)  The cohomology generated by the set of vector bundles over some topological space or scheme.
 * 1)  The cohomology generated by the set of vector bundles over some topological space or scheme.

Usage notes

 * In mathematics:
 * Following 's 1957 publication of a proof of the, K-theory was developed as a subfield of algebraic topology (notably in relation to C*-algebra theory). This subfield is now known as.
 * Subsequently, K-theory was generalised as a subfield of algebraic geometry, now often called.
 * 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 (aka K-theory with local coefficients) is the basis of an application called K-theory classification, by which certain (hypothetical) objects are classified.

Hyponyms

 * algebraic K-theory, topological K-theory

Derived terms

 * algebraic K-theory
 * complex K-theory
 * K-theory classification
 * Morava K-theory
 * real K-theory
 * topological K-theory
 * twisted K-theory