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KR-theory
In mathematics, KR-theory is a variant of topological K-theory defined for spaces with an involution. It was introduced by , motivated by applications to the Atiyah–Singer index theorem for real elliptic operators.
==Definition==
A ''real space'' is a defined to be a topological space with an involution. A real vector bundle over a real space ''X'' is defined to be a complex vector bundle ''E'' over ''X'' that is also a real space, such that the natural maps from ''E'' to ''X'' and from C×''E'' to ''E'' commute with the involution, where the involution acts as complex conjugation on C. (This differs from the notion of a complex vector bundle in the category of Z/2Z spaces, where the involution acts trivially on C.)
The group ''KR''(''X'') is the Grothendieck group of finite-dimensional real vector bundles over the real space ''X''.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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