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Computing the abelian heap of unpointed stable homotopy classes of maps

Lukáš Vokřínek (2013)

Archivum Mathematicum

An algorithmic computation of the set of unpointed stable homotopy classes of equivariant fibrewise maps was described in a recent paper [4] of the author and his collaborators. In the present paper, we describe a simplification of this computation that uses an abelian heap structure on this set that was observed in another paper [5] of the author. A heap is essentially a group without a choice of its neutral element; in addition, we allow it to be empty.

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 .

Étude des Γ -structures de codimension 1 sur la sphère S 2

Claude Roger (1973)

Annales de l'institut Fourier

Cet article contient une démonstration géométrique simple de π 2 ( B Γ 1 r ) = 0 pour r = 0 , ∞ .Ce résultat (démontré aussi par Mather comme corollaire d’un théorème beaucoup plus général) apparaît comme une conséquence du théorème de Michael Herman : Diff S 1 [ Diff S 1 , Diff S 1 ] = 0 .L’appendice contient une étude des Γ structures sur les surfaces et un résultat sur la cohomologie de Diff S 1 .

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