WEDNESDAY, June 18–th, 12:30–13:30

K-theories and Cohomology Theories

Grothendieck introduced K–theory in his study of vector bundles and used this to formulate a remarkable relationship between vector bundles and algebraic cycles on a smooth algebraic variety. Atiyah and Hirzebruch studied the analogous topological K–theory and related it to the singular cohomology of a finite dimensional C.W. complex. Quillen developed higher algebraic K–theory and established another relationship between K–theory and algebraic cycles. Bloch and Suslin-Voevodsky introduced algebraic cohomology theories based on algebraic cycles, whereas Friedlander–Lawson studied semi–topological analogues for real and complex varieties. Friedlander–Walker introduced semi–topological K–theory based on the familiar notion of algebraic equivalence.
We discuss interconnections among these constructions as well as various examples which have been computed.