In mathematics, a bivariant theory was introduced by Fulton and MacPherson (Fulton ' MacPherson 1981) harv error: no target: CITEREFFultonMacPherson1981.

"operational Chow ring" and more generally a bivariant theory associated to any morphism of schemes.

A bivariant theory is a pair of covariant and contravariant.

A further development in this is a bivariant version of K-theory called KK-theory, which has a composition product.

This, in turn, led to K-homology, Kasparov's bivariant KK-theory, and, more recently, Connes and Higson's E-theory.

The last one is very close to K-theory as it is endowed with a bivariant Chern character from KK-theory.

Springer Verlag 1998 With Joachim Cuntz, Ralf Meyer: Topological and bivariant K-theory, Birkhauser 2007 Editor Robert Doran, Greg Friedman: Superstrings.

The localized Chern class of this complex is a class in the bivariant Chow group of X ⊂ Y {\displaystyle X\subset Y} defined as follows.

δ through the use of standard least squares methods for determining a bivariant regression plane.

Paley-Wiener theorem by characterizing the spherical transforms of smooth K-bivariant functions of compact support on G.