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Real projective spaces are nonfibrators

โœ Scribed by R.J. Daverman

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
62 KB
Volume
94
Category
Article
ISSN
0166-8641

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โœฆ Synopsis

Fibrators are manifolds which, in context, automatically induce approximate fibrations. This paper sets forth a new method for constructing nonfibrators, by establishing that a closed connected manifold N fails to be a codimension k + 1 fibrator provided there exists a homeomorphism h of N ร— S k onto itself such that proj โ€ข h : N ร— {point} โ†’ N is not a homotopy equivalence. Consequently, real projective n-space fails to be a codimension n + 1 fibrator, and certain manifolds covered by S 3 fail to be codimension 4 fibrators.

๐Ÿ“œ SIMILAR VOLUMES

If vector spaces are projective modules
If vector spaces are projective modules then multiple choice holds
โœ Paul Howard ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 90 KB

We show that the assertion that every vector space is a projective module implies the axiom of multiple choice and that the reverse implication does not hold in set theory weakened to permit the existence of atoms.