Semi-topologization in motivic homotopy theory and applications
arXiv:1302.2218 · doi:10.2140/agt.2015.15.823
Abstract
We study the semi-topologization functor of Friedlander-Walker from the perspective of motivic homotopy theory. We construct a triangulated endo-functor on the stable motivic homotopy category $\mathcal{SH}(\C)$, which we call \emph{homotopy semi-topologization}. As applications, we discuss the representability of several semi-topological cohomology theories in $\mathcal{SH}(\C)$, a construction of a semi-topological analogue of algebraic cobordism, and a construction of Atiyah-Hirzebruch type spectral sequences for this theory.
v1: 41 pages; v2: 39 pages. The 'idempotence' part of v1 deleted, with some minor revision; v3: 24 pages. Largely rewritten and compactified. A variation of this version is accepted to appear in Algebraic & Geometric Topology