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A F -algebras and topology of mapping tori

Igor Nikolaev (2015)

Czechoslovak Mathematical Journal

The paper studies applications of C * -algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of A F -algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding A F -algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension 2 , 3 and 4 . In conclusion, we consider two numerical examples illustrating our main results.

Applications depuis K ( ℤ / p , 2 ) et une conjecture de N. Kuhn

Gérald Gaudens, Lionel Schwartz (2013)

Annales de l’institut Fourier

Dans cet article on démontre une conjecture de N. Kuhn : si la cohomologie singulière modulo un nombre premier p d’un espace est finiment engendrée comme module sur l’algèbre de Steenrod, alors elle est finie. On donne aussi des formes plus fortes de ce résultat. Le second auteur en avait déjà donné une démonstration dans un article précédent. Cependant dans le cas d’un nombre premier impair la preuve comportait une lacune sans hypothèse supplémentaire sur la cohomologie de l’espace, du type de...

Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds

Hajime Sato (1972)

Annales de l'institut Fourier

We aim at constructing a PL-manifold which is cellularly equivalent to a given homology manifold M n . The main theorem says that there is a unique obstruction element in H n - 4 ( M , ℋ 3 ) , where ℋ 3 is the group of 3-dimensional PL-homology spheres modulo those which are the boundary of an acyclic PL-manifold. If the obstruction is zero and M is compact, we obtain a PL-manifold which is simple homotopy equivalent to M .

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