Bott and Taubes constructed knot invariants by considering a bundle over the space of knots and performing integration along the fiber. This method was subsequently used to construct real cohomology classes in spaces of knots in R^n, n > 3. Replacing integration of differential forms by a Pontrjagin-Thom construction, I have constructed cohomology classes with arbitrary coefficients. Motivated by work of Budney and F. Cohen on the homology of the space of long knots in R^3, I have also proven a product formula for these classes with respect to connect-sum. If time permits, I will outline work in progress towards explicit calculations using cosimplicial models for knot spaces coming from the Goodwillie-Weiss embedding calculus. |