Secondary homotopy groups supplement the structure of classical homotopy groups. They yield a track functor on the track ...

Without doubts, calculating homotopy groups of spheres is one of the main open problems in Algebraic Topology. After Toda ...

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.

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 category.

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.

We consider the following problems in a well generated triangulated category T . Let α be a regular cardinal and T α ⊂ T ...

We construct a topological cellular operad such that the algebras over its cellular chains are the homotopy unital A∞-algebras of Fukaya-Oh-Ohta-Ono.