A topological Chern character for matrix factorizations

Abstract

For $Y$ a quasi-projective complex variety and $w:Y\to \mathbb{C}$ a regular function, we construct a Chern character from the Grothendieck group of the category of matrix factorizations of $w$ to the critical cohomology of $w$, and show that it factors through a certain topological $K$-theory group. We prove a Grothendieck-Riemann-Roch theorem with respect to this Chern character, and verify several functorial properties.

32 pages, comments welcome