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Generalized universal covering spaces and the shape group

Hanspeter Fischer, Andreas Zastrow (2007)

Fundamenta Mathematicae

If a paracompact Hausdorff space X admits a (classical) universal covering space, then the natural homomorphism φ: π₁(X) → π̌₁(X) from the fundamental group to its first shape homotopy group is an isomorphism. We present a partial converse to this result: a path-connected topological space X admits a generalized universal covering space if φ: π₁(X) → π̌₁(X) is injective. This generalized notion of universal covering p: X̃ → X enjoys most of the usual properties, with the possible exception of evenly...

Generating varieties for the triple loop space of classical Lie groups

Yasuhiko Kamiyama (2003)

Fundamenta Mathematicae

For G = SU(n), Sp(n) or Spin(n), let C G ( S U ( 2 ) ) be the centralizer of a certain SU(2) in G. We have a natural map J : G / C G ( S U ( 2 ) ) Ω ³ G . For a generator α of H ( G / C G ( S U ( 2 ) ) ; / 2 ) , we describe J⁎(α). In particular, it is proved that J : H ( G / C G ( S U ( 2 ) ) ; / 2 ) H ( Ω ³ G ; / 2 ) is injective.

G-functors, G-posets and homotopy decompositions of G-spaces

Stefan Jackowski, Jolanta Słomińska (2001)

Fundamenta Mathematicae

We describe a unifying approach to a variety of homotopy decompositions of classifying spaces, mainly of finite groups. For a group G acting on a poset W and an isotropy presheaf d:W → (G) we construct a natural G-map h o c o l i m d G / d ( - ) | W | which is a (non-equivariant) homotopy equivalence, hence h o c o l i m d E G × G F d E G × G | W | is a homotopy equivalence. Different choices of G-posets and isotropy presheaves on them lead to homotopy decompositions of classifying spaces. We analyze higher limits over the categories associated to isotropy presheaves...

Groupoïde fondamental et d'holonomie de certains feuilletages réguliers

María C. Lasso de la Vega (1989)

Publicacions Matemàtiques

Let M be a manifold with a regular foliation F. We recall the construction of the fundamental groupoid and the homotopy groupoid associated to F. We describe some interesting particular cases and give some glueing techniques. We characterize the cases where these groupoids are Hausdorff spaces.We study in particular both groupoids associated to foliations with Reeb components.

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