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Quelques contre-exemples pour la LS catégorie d'une algèbre de cochaînes

Elhassan Idrissi (1991)

Annales de l'institut Fourier

À toute algèbre de cochaînes A sont associés les invariants numériques suivants : bi M cat ( A ) , r M cat ( A ) et l M cat ( A ) qui approximent, pour tout corps k et lorsque A = C * ( X ; k ) , la catégorie au sens de Lusternik-Schnirelmann de l’espace X . Nous montrons dans cet article que ces trois invariants sont deux à deux distincts.

The construction of 3-Lie 2-algebras

Chunyue Wang, Qingcheng Zhang (2018)

Czechoslovak Mathematical Journal

We construct a 3-Lie 2-algebra from a 3-Leibniz algebra and a Rota-Baxter 3-Lie algebra. Moreover, we give some examples of 3-Leibniz algebras.

The universal functorial Lefschetz invariant

Wolfgang Lück (1999)

Fundamenta Mathematicae

We introduce the universal functorial Lefschetz invariant for endomorphisms of finite CW-complexes in terms of Grothendieck groups of endomorphisms of finitely generated free modules. It encompasses invariants like Lefschetz number, its generalization to the Lefschetz invariant, Nielsen number and L 2 -torsion of mapping tori. We examine its behaviour under fibrations.

The Vietoris system in strong shape and strong homology

Bernd Günther (1992)

Fundamenta Mathematicae

We show that the Vietoris system of a space is isomorphic to a strong expansion of that space in the Steenrod homotopy category, and from this we derive a simple description of strong homology. It is proved that in ZFC strong homology does not have compact supports, and that enforcing compact supports by taking limits leads to a homology functor that does not factor over the strong shape category. For compact Hausdorff spaces strong homology is proved to be isomorphic to Massey's homology.

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