Semitopologization in motivic homotopy theory and applications

Krishna, Amalendu¹ ; Park, Jinhyun²

¹School of Mathematics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Colaba, Mumbai 400 005, India
²Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701, South Korea

Algebraic and Geometric Topology, Tome 15 (2015) no. 2, pp. 823-861

Résumé

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.

Détail

DOI : 10.2140/agt.2015.15.823

Classification : 14F42, 19E08
Keywords: motivic homotopy, semitopologization, $K$–theory, morphic cohomology, algebraic cobordism

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