Doosung Park (Universität Zürich) Calculus of fractions and box-homotopy theory

To extend A¹-homotopy theory so that non A¹-invariant cohomology theories like algebraic K-theory and algebraic de Rham cohomology are representable, the so-called box-invariance has been suggested. However, the usual Sing construction for box does not work well since box is not an interval object. In this talk, I will give a new Sing construction for box using calculus of fractions. This is a partial result of an ongoing project joint with Federico Binda and Paul Arne Østvær.