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Products of hopfian manifolds and codimension-2 fibrators

โœ Scribed by Robert J. Daverman; Young Ho Im; Yongkuk Kim

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
149 KB
Volume
103
Category
Article
ISSN
0166-8641

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โœฆ Synopsis

We describe several conditions under which the product of hopfian manifolds is another hopfian manifold. As applications, the product F ร— A of a closed hopfian n-manifold F and a closed orientable aspherical m-manifold A is hopfian when either ฯ€ 1 (F ) is solvable and ฯ‡(A) = 0 or ฯ€ 1 (F ) is finite. Also, the product of any rational homology n-sphere ฮฃ n for which ฯ€ 1 (ฮฃ n ) is finite and a closed orientable n-manifold N with ฯ€ i (N) = 0 for 1 < i < n -1 is hopfian. Using such facts we investigate conditions under which products of codimension-2 (orientable) fibrators are again codimension-2 (orientable) fibrators.

๐Ÿ“œ SIMILAR VOLUMES

Strongly hopfian manifolds as codimensio
Strongly hopfian manifolds as codimension-2 fibrators
โœ Kim Yongkuk ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 613 KB

If a closed n-manifold N has a 2-l covering, we consider the covering space E of N corresponding to H, where H is the intersection of all subgroups H, of index 2 in ~1 (N), i.e., H = n,,, Hi with [T,(N) : Hi] = 2 for i E I. We will show that if nt(N) is residually finite, x(N) # 0, and fi is hopfian

Manifolds with hyperhopfian fundamental
Manifolds with hyperhopfian fundamental group as codimension-2 fibrators
โœ Yongkuk Kim ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 77 KB

Every hopfian n-manifold N with hyperhopfian fundamental group is known to be a codimension-2 orientable fibrator. In this paper, we generalize to the non-orientable setting by considering the covering space N of N corresponding to H , where H is the intersection of all subgroups H i of index 2 in ฯ€

Manifolds with finite cyclic fundamental
Manifolds with finite cyclic fundamental groups and codimension 2 fibrators
โœ Naotsugu Chinen ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 123 KB

A closed connected n-manifold N is called a codimension 2 fibrator (codimension 2 orientable fibrator, respectively) if each proper map p : M โ†’ B on an (orientable, respectively) (n+2)-manifold M each fiber of which is shape equivalent to N is an approximate fibration. Let r be a nonnegative integer