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Finite spaces and the universal bundle of a group

Peter Witbooi (1997)

Commentationes Mathematicae Universitatis Carolinae

We find sufficient conditions for a cotriad of which the objects are locally trivial fibrations, in order that the push-out be a locally trivial fibration. As an application, the universal G -bundle of a finite group G , and the classifying space is modeled by locally finite spaces. In particular, if G is finite, then the universal G -bundle is the limit of an ascending chain of finite spaces. The bundle projection is a covering projection.

Finite-dimensional spaces in resolving classes

Jeffrey Strom (2012)

Fundamenta Mathematicae

Using the theory of resolving classes, we show that if X is a CW complex of finite type such that m a p ( X , S 2 n + 1 ) for all sufficiently large n, then map⁎(X,K) ∼ ∗ for every simply-connected finite-dimensional CW complex K; and under mild hypotheses on π₁(X), the same conclusion holds for all finite-dimensional complexes K. Since it is comparatively easy to prove the former condition for X = Bℤ/p (we give a proof in an appendix), this result can be applied to give a new, more elementary proof of the Sullivan conjecture....

Fixed points on Klein bottle fiber bundles over the circle

D. L. Gonçalves, D. Penteado, J. P. Vieira (2009)

Fundamenta Mathematicae

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S¹ for spaces which are fiber bundles over S¹ and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S¹ has been solved recently.

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