๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Manifolds with hyperhopfian fundamental group as codimension-2 fibrators

โœ Scribed by Yongkuk Kim

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
77 KB
Volume
96
Category
Article
ISSN
0166-8641

No coin nor oath required. For personal study only.

โœฆ Synopsis

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€ 1 (N). First, we will show that if ฯ€ 1 (N) is hyperhopfian and N is hopfian, then N is a codimension-2 fibrator. Then we get several results about codimension-2 fibrators as corollaries.

๐Ÿ“œ SIMILAR VOLUMES

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

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