Semitopologization in motivic homotopy theory and applications

Krishna, Amalendu; Park, Jinhyun

doi:10.2140/agt.2015.15.823

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Semitopologization in motivic homotopy theory and applications

Amalendu Krishna and Jinhyun Park

Algebraic & Geometric Topology 15 (2015) 823–861

DOI: 10.2140/agt.2015.15.823

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 $S ℋ (ℂ)$ , which we call homotopy semitopologization. As applications, we discuss the representability of several semitopological cohomology theories in $S ℋ (ℂ)$ , 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

Mathematical Subject Classification 2010

Primary: 14F42

Secondary: 19E08

References

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

Volume 15, issue 2 (2015)