Volume 15, issue 2 (2015)

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Semitopologization in motivic homotopy theory and applications

Amalendu Krishna and Jinhyun Park

Algebraic & Geometric Topology 15 (2015) 823–861
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 $\mathsc{S}\mathsc{ℋ}\left(ℂ\right)$, which we call homotopy semitopologization. As applications, we discuss the representability of several semitopological cohomology theories in $\mathsc{S}\mathsc{ℋ}\left(ℂ\right)$, a construction of a semitopological analogue of algebraic cobordism and a construction of Atiyah–Hirzebruch type spectral sequences for this theory.

Keywords
motivic homotopy, semitopologization, $K$–theory, morphic cohomology, algebraic cobordism
Primary: 14F42
Secondary: 19E08
Publication
Received: 20 January 2014
Revised: 26 August 2014
Accepted: 9 October 2014
Published: 22 April 2015
Authors
 Amalendu Krishna School of Mathematics Tata Institute of Fundamental Research 1 Homi Bhabha Road, Colaba Mumbai 400 005 India Jinhyun Park Department of Mathematical Sciences KAIST 291 Daehak-ro, Yuseong-gu Daejeon, 305-701 South Korea