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Coherent and strong expansions of spaces coincide

Sibe Mardešić (1998)

Fundamenta Mathematicae

In the existing literature there are several constructions of the strong shape category of topological spaces. In the one due to Yu. T. Lisitsa and S. Mardešić [LM1-3] an essential role is played by coherent polyhedral (ANR) expansions of spaces. Such expansions always exist, because every space admits a polyhedral resolution, resolutions are strong expansions and strong expansions are always coherent. The purpose of this paper is to prove that conversely, every coherent polyhedral (ANR) expansion...

Coherent functors in stable homotopy theory

Henning Krause (2002)

Fundamenta Mathematicae

Coherent functors 𝓢 → Ab from a compactly generated triangulated category into the category of abelian groups are studied. This is inspired by Auslander's classical analysis of coherent functors from a fixed abelian category into abelian groups. We characterize coherent functors and their filtered colimits in various ways. In addition, we investigate certain subcategories of 𝓢 which arise from families of coherent functors.

Co-H-structures on equivariant Moore spaces

Martin Arkowitz, Marek Golasiński (1994)

Fundamenta Mathematicae

Let G be a finite group, 𝕆 G the category of canonical orbits of G and A : 𝕆 G → 𝔸 b a contravariant functor to the category of abelian groups. We investigate the set of G-homotopy classes of comultiplications of a Moore G-space of type (A,n) where n ≥ 2 and prove that if such a Moore G-space X is a cogroup, then it has a unique comultiplication if dim X < 2n - 1. If dim X = 2n-1, then the set of comultiplications of X is in one-one correspondence with E x t n - 1 ( A , A ⊗ A ) . Then the case G = ℤ p k leads to an example of infinitely...

Combinatoire des simplexes sans singularités I. Le cas différentiable

Jean Cerf (1998)

Annales de l'institut Fourier

On définit le bicomplexe C • , • , extension naturelle du complexe C engendré par un ensemble simplicial Γ . Ceci permet de définir la notion de ruban de base un cycle de C . La somme directe de l’homologie des colonnes de C • , • contient, outre l’homologie de C , des groupes dans lesquels se trouvent les obstructions à l’existence de rubans. Si Γ est un sous-ensemble simplicial, stable par subdivision, de l’ensemble des simplexes singuliers d’un espace topologique, l’existence de rubans entraîne l’invariance...

Combinatoric of syzygies for semigroup algebras.

Emilio Briales, Pilar Pisón, Antonio Campillo, Carlos Marijuán (1998)

Collectanea Mathematica

We describe how the graded minimal resolution of certain semigroup algebras is related to the combinatorics of some simplicial complexes. We obtain characterizations of the Cohen-Macaulay and Gorenstein conditions. The Cohen-Macaulay type is computed from combinatorics. As an application, we compute explicitly the graded minimal resolution of monomial both affine and simplicial projective surfaces.

Currently displaying 21 – 40 of 52