Volume 15, issue 2 (2015)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 S(), which we call homotopy semitopologization. As applications, we discuss the representability of several semitopological cohomology theories in S(), 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