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Artículo
The symmetric action on secondary homotopy groups
(The Belgian Mathematical Society, 2008-11)
We show that the symmetric track groups Sym(n), which are extensions of the symmetric groups Sym(n) associated to the second Stiefel-Whitney class, act as crossed modules on the secondary homotopy groups of a pointed space.
Artículo
Representation theory of some infinite-dimensional algebras arising in continuously controlled algebra and topology
(Springer, 2004)
In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the ...
Artículo
The 1-type of a Waldhausen K-theory spectrum
(Elsevier, 2007-12-01)
We give a small functorial algebraic model for the 2-stage Postnikov section of the K-theory spectrum of a Waldhausen category and use our presentation to describe the multiplicative structure with respect to biexact functors.
Artículo
The characteristic cohomology class of a triangulated category
(2005)
The concept of a triangulated homotopy category can be canonically lifted to the level of a groupoid-enriched category. This way two natural axioms on track triangles replace the four somewhat obscure axioms of a triangulated ...
Artículo
Maltsiniotis's first conjecture for K1
(Duke University Press, 2008)
We show that K1(E) of an exact category E agrees with K1(DE) of the associated triangulated derivator DE. More generally we show that K1(W) of a Waldhausen category W with cylinders and a saturated class of weak equivalences ...
Artículo
Toda brackets and cup-one squares for ring spectra
(Taylor & Francis, 2009)
In this paper we prove the laws of Toda brackets on the homotopy groups of a connective ring spectrum and the laws of the cup-one square in the homotopy groups of a commutative connective ring spectrum.
Artículo
Triangulated categories without models
(Springer, 2007-11)
We exhibit examples of triangulated categories which are neither the stable category of a Frobenius category nor a full triangulated subcategory of the homotopy category of a stable model category. Even more drastically ...
Artículo
Secondary homotopy groups
(De Gruyter, 2008-07)
Secondary homotopy groups supplement the structure of classical homotopy groups. They yield a track functor on the track category of pointed spaces compatible with fiber sequences, suspensions and loop spaces. They also ...
Artículo
On the functoriality of cohomology of categories
(Elsevier, 2006-03)
In this paper we show that the Baues-Wirsching complex used to define cohomology of categories is a 2-functor from a certain 2-category of natural systems of abelian groups to the 2-category of chain complexes, chain ...
Artículo
Smash products for secondary homotopy groups
(Springer, 2008-10)
We construct a smash product operation on secondary homotopy groups yielding the structure of a lax symmetric monoidal functor. Applications on cup-one products, Toda brackets and Whitehead products are considered.