This paper became the starting point of investigations of homology for more general spaces than merely finite complexes or open subsets of R

Abstract. We prove that the infinite tensor power of a unital separable C ∗-algebra absorbs the Jiang-Su algebraZ tensorially if and only if it contains, unitally, a subhomogeneous algebra without characters. This yields a succinct universal property for Z in a category so large that there are no unital separable C ∗-algebras without characters known to lie outside it. This category moreover contains the vast majority of our stock-in-trade separable amenable C ∗-algebras, and is closed under passage to separable superalgebras and quotients, and hence to unital tensor products, unital direct limits, and crossed products by countable discrete groups. One consequence of our main result is that strongly self-absorbing ASH algebras areZ-stable, and therefore satisfy the hypotheses of a recent classification theorem of W. Winter. One concludes thatZ is the only projectionless strongly self-absorbing ASH algebra, completing the classification of strongly self-absorbing ASH algebras. 1.

sanitarium at Innsbruck after a brief illness. The mathematical community has lost a well-known researcher. Vietoris was the recipient of several high awards.

Abstract not found

Abstract. Let S(R) be an o-minimal structure over R, T ⊂ R k1+k2+ℓ a closed definable set, and π1: R k1+k2+ℓ

Let G be a compact connected Lie group and H the centralizer of a oneparameter subgroup. We obtain a unified formula that expresses Steenrod operations on Schubert classes in the flag manifold G/H in term of Cartan numbers of G.

A unified formula for Steenrod operations in flag manifolds

A unified formula for Steenrod operations in flag manifolds

Abstract. An intrinsic, combinatorial homotopy theory has been developed in [G3] for simplicial complexes; these form a cartesian closed subcategory in the topos!Smp of symmetric simplicial sets, or presheaves on the category!å of finite, positive cardinals. We show here how this homotopy theory can be extended to the topos itself,!Smp. As a crucial advantage, the fundamental groupoid Π1:!Smp = Gpd is left adjoint to a natural functor M1: Gpd =!Smp, the symmetric nerve of a groupoid, and preserves all colimits – a strong van Kampen property. Similar results hold in all higher dimensions. Analogously, a notion of (non-reversible) directed homotopy can be developed in the ordinary simplicial topos Smp, with applications to image analysis as in [G3]. We have now a homotopy n-category functor ↑Πn: Smp = n-Cat, left adjoint to a nerve Nn = n-Cat(↑Πn(∆[n]), –). This construction can be applied to various presheaf categories; the basic requirements seem to be: finite products of representables are finitely presentable and there is a representable 'standard interval'.

In this note, working in the context of simplicial sets [17], we give a detailed study of the complexity for computing chain level Steenrod squares [20, 21], in terms of the number of face operators required. This analysis is based on the combinatorial formulation given in [5]. As an application, we give here an algorithm for computing cup–i products over integers on a simplicial complex at chain level. 1