منابع مشابه
SOME EXAMPLES OF SPHERE BUNDLES OVER SPHERES WHICH ARE LOOP SPACES mod/? BY JOHN EWING
In this note we give sufficient conditions that certain sphere bundles over spheres, denoted Bn(p), are of the homotopy type of loop spaces mod/? for p an odd prime. The method is to construct a classifying space for the /?-profinite completion of Bn(p) by collapsing an Eilenberg-Mac Lane space by the action of a certain finite group. We say that a space X has some property mod/? if the localiz...
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These results were discovered in an attempt to embed real projective spaces. The well-known Hopf fiberings of Pu and Pi give the following representations of these spaces: Pi is a fiber space over S4 with P% as fiber, and Pu is a fiber space over S8 with P7 as fiber. Since any embedding of Pz in R6 has a trivial normal bundle [ó], Theorem 1.2 applies for Pi. Theorem 1.1 applies for Pu and, henc...
متن کاملBundles over Quantum RealWeighted Projective Spaces
The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1)-bundles over quantum real weighted projective spaces are constructed. As the spaces in question fall into two separate classes, the negative or odd class that generalises quantum real projective planes and the positive or even class that genera...
متن کاملTiling Spaces Are Cantor Set Fiber Bundles
We prove that fairly general spaces of tilings of R are fiber bundles over the torus T , with totally disconnected fiber. This was conjectured (in a weaker form) in [W3], and proved in certain cases. In fact, we show that each such space is homeomorphic to the d-fold suspension of a Z subshift (or equivalently, a tiling space whose tiles are marked unit d-cubes). The only restrictions on our ti...
متن کاملVector Bundles over Classifying Spaces of Compact Lie Groups
The completion theorem of Atiyah and Segal [AS] says that the complex K-theory group K(BG) of the classifying space of any compact Lie group G is isomorphic to R(G)̂ : the representation ring completed with respect to its augmentation ideal. However, the group K(BG) = [BG,Z × BU ] does not directly contain information about vector bundles over the infinite dimensional complex BG itself. The purp...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1971
ISSN: 0022-4049
DOI: 10.1016/0022-4049(71)90010-7