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Cobordisme fibré et approximation d’une sous-variété singulière par des sous-variétés C ∞

André Didierjean (1983)

Annales de l'institut Fourier

Dans cet article, on montre comment le cobordisme d’applications et le cobordisme fibré fournissent les obstructions à des problèmes de lissage topologique de singularités avec un lieu singulier compact. On calcule dans le cas des petites dimensions les groupes de cobordisme fibré. Les résultats connus sur le cobordisme fibré ou sur son image dans le cobordisme d’application permettent le calcul d’un certain nombre de ces obstructions.

Cobordisms of fold maps of 2k+2-manifolds into ℝ 3 k + 2

Tamás Terpai (2008)

Banach Center Publications

We calculate the group of cobordisms of k-codimensional maps into Euclidean space with no singularities more complicated than fold for a 2k+2-dimensional source manifold in both oriented and unoriented cases.

Cochains and homotopy type

Michael A. Mandell (2006)

Publications Mathématiques de l'IHÉS

Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E∞ algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E∞ algebras is faithful but not full.

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.

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