Now showing items 1-10 of 26
K-theory of derivators revisited [Article]
(Mathematical Sciences Publishers, 2017)
We define a K-theory for pointed right derivators and show that it agrees with Waldhausen K-theory in the case where the derivator arises from a good Waldhausen category. This K-theory is not invariant under general ...
On determinant functors and K-theory [Article]
(Universitat Autònoma de Barcelona, 2015)
We extend Deligne’s notion of determinant functor to Waldhausen categories and (strongly) triangulated categories. We construct explicit universal determinant functors in each case, whose target is an algebraic model for ...
The symmetric action on secondary homotopy groups [Article]
(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.
Moduli spaces of algebras over non-symmetric operads [Article]
In this paper we study spaces of algebras over an operad (nonsymmetric) in symmetric monoidal model categories. We first compute the homotopy fiber of the forgetful functor sending an algebra to its underlying object, ...
The algebra of secondary homotopy operations in ring spectra [Article]
(London Mathematical Society, 2011)
The primary algebraic model of a ring spectrum R is the ring π∗R of homotopy groups. We introduce the secondary model π∗,∗R which has the structure of a secondary analogue of a ring. The homology of π∗,∗R is π∗R and ...
Torsion homology and cellular approximation [Article]
(Mathematical Sciences Publishers, 2019-02-06)
We describe the role of the Schur multiplier in the structure of the p-torsion of discrete groups. More concretely, we show how the knowledge of H2G allows us to approximate many groups by colimits of copies of p-groups. ...
Entrevista a Isabel Fernández, conferenciante invitada al ICM 2010 [Article]
(Real Sociedad Matematica Española, 2010)
Isabel Fernández, de la Universidad de Sevilla, es conferenciante invitada junto con Pablo Mira (Universidad Politécnica de Cartagena) a la sección de Geometría del próximo ICM, que se celebrará en agosto en Hyderabad ...
Smash products for secondary homotopy groups [Article]
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.
Triangulated categories without models [Article]
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 ...
Secondary homotopy groups [Article]
(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 ...