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29
The Incommunicability of Content
 Mind
, 1966
"... 1. Setting up the foundations 3 2. The EilenbergSteenrod axioms 4 3. Stable and unstable homotopy groups 5 4. Spectral sequences and calculations in homology and homotopy 6 ..."
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1. Setting up the foundations 3 2. The EilenbergSteenrod axioms 4 3. Stable and unstable homotopy groups 5 4. Spectral sequences and calculations in homology and homotopy 6
Nielsen numbers of nvalued fiber maps
 Journal of Fixed Point Theory and Applications
, 2008
"... The Nielsen number for nvalued multimaps, defined by Schirmer, has been calculated only for the circle. A concept of nvalued fiber map on the total space of a fibration is introduced. A formula for the Nielsen numbers of nvalued fiber maps of fibrations over the circle reduces the calculation to ..."
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The Nielsen number for nvalued multimaps, defined by Schirmer, has been calculated only for the circle. A concept of nvalued fiber map on the total space of a fibration is introduced. A formula for the Nielsen numbers of nvalued fiber maps of fibrations over the circle reduces the calculation to the computation of Nielsen numbers of singlevalued maps. If the fibration is orientable, the product formula for singlevalued fiber maps fails to generalize, but a “semiproduct formula ” is obtained. In this way, the class of nvalued multimaps for which the Nielsen number can be computed is substantially enlarged. Subject Classification 55M20, 54C60 1
On higher dimensional HirzebruchJung singularities
 Rev. Mat. Complut
"... A germ of normal complex analytical surface is called a HirzebruchJung singularity if it is analytically isomorphic to the germ at the 0dimensional orbit of an affine toric surface. Two such germs are known to be isomorphic if and only if the toric surfaces corresponding to them are equivariantly ..."
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A germ of normal complex analytical surface is called a HirzebruchJung singularity if it is analytically isomorphic to the germ at the 0dimensional orbit of an affine toric surface. Two such germs are known to be isomorphic if and only if the toric surfaces corresponding to them are equivariantly isomorphic. We extend this result to higherdimensional HirzebruchJung singularities, which we define to be the germs analytically isomorphic to the germ at the 0dimensional orbit of an affine toric variety determined by a lattice and a simplicial cone of maximal dimension. We deduce a normalization algorithm for quasiordinary hypersurface singularities. 2000 Mathematics Subject Classification. Primary 32S10; Secondary 14M25. 1
A History of Duality in Algebraic Topology
"... This paper became the starting point of investigations of homology for more general spaces than merely finite complexes or open subsets of R ..."
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This paper became the starting point of investigations of homology for more general spaces than merely finite complexes or open subsets of R
Biography
, 2002
"... sanitarium at Innsbruck after a brief illness. The mathematical community has lost a wellknown researcher. Vietoris was the recipient of several high awards. ..."
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sanitarium at Innsbruck after a brief illness. The mathematical community has lost a wellknown researcher. Vietoris was the recipient of several high awards.
→ R
"... Abstract. Let S(R) be an ominimal structure over R, T ⊂ R k1+k2+ℓ a closed definable set, and π1: R k1+k2+ℓ ..."
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Abstract. Let S(R) be an ominimal structure over R, T ⊂ R k1+k2+ℓ a closed definable set, and π1: R k1+k2+ℓ
Steenrod operations on Schubert classes
, 2003
"... 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. ..."
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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.
1 Higher fundamental functors for simplicial sets ( *)
, 2000
"... 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 ..."
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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 (nonreversible) directed homotopy can be developed in the ordinary simplicial topos Smp, with applications to image analysis as in [G3]. We have now a homotopy ncategory functor ↑Πn: Smp = nCat, left adjoint to a nerve Nn = nCat(↑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'.
Rocío González–Díaz, Pedro Real Universidad de Sevilla, Depto. de Matemática Aplicada I,
, 2001
"... 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 ..."
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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