Motivic cell structures

By Daniel Dugger, Daniel Isaksen. 2003

108 citations recorded by the source corpus.

An object in motivic homotopy theory is called cellular if it can be built out of motivic spheres using homotopy colimit constructions. We explore some examples and consequences of cellularity. We explain why the algebraic K-theory and algebraic cobordism spectra are both cellular, and prove some Kunneth theorems for cellular objects. AMS Classification 55U35; 14F42

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8af2f4bed8849351b170fce00da38bf602b14e33

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

CHOW GROUPS, CHOW COHOMOLOGY, AND LINEAR VARIETIES (2014, background): “I also added some papers to the bibliography which refer to the preprint version of this paper, and which develop the ideas further [7, 10, 14, 17, 23].”
The motive of a classifying space (2014, methodology): “The category of mixed Tate motives is analogous to the category of cellular spectra in the stable homotopy category SH.k/ studied by Voevodsky [60] and Dugger and Isaksen [19].”
Slices of hermitian $K$–theory and Milnor's conjecture on quadratic forms (2013, background): “Thus the Tate motivic spectrum 2 KGL=22 is cellular in the sense of [8], since KQ is cellular [47].”
The motivic adams spectral sequence (2009, methodology): “The smallest full subcategory of the motivic stable homotopy category that satisfies (i)–(iii) is denoted hSi, and equals the category of cellular spectra of [7].”
On the motivic spectra representing algebraic cobordism and algebraic $K$-theory (2007, background): “This is an immediate consequence of the motivic Künneth spectral sequence of DuggerIsaksen [5].”