Semitopologization in motivic homotopy theory and applications

Abstract

We study the semitopologization functor of Friedlander and Walker from the perspective of motivic homotopy theory. We construct a triangulated endofunctor on the stable motivic homotopy category SH(ℂ), which we call homotopy semitopologization. As applications, we discuss the representability of several semitopological cohomology theories in SH(ℂ), a construction of a semitopological analogue of algebraic cobordism and a construction of Atiyah–Hirzebruch type spectral sequences for this theory.