The ¯∂ Operator in Holomorphic K-Theory
Article - Open Access
Homology, Homotopy and Applications
The holomorphic (or semi-topological) K-theory of a smooth projective variety sits between the algebraic K-theory of the variety and the topological K-theory of the underlying topological space. We describe how to define a family of dbar operators on holomorphic K-theory in a manner analogous to Atiyah’s construction of a family of elliptic operators in topological K-theory. In the process, we prove a result akin to Bott periodicity for holomorphic mapping spaces. These results first appeared in the author’s Stanford University Ph.D. thesis under the direction of Ralph Cohen.
(2006). The ¯∂ Operator in Holomorphic K-Theory. Homology, Homotopy and Applications, 8(1), 187-210.
Available at: http://scholarworks.merrimack.edu/mth_facpub/5