Manifolds with finite cyclic fundamental groups and codimension 2 fibrators

✍ Scribed by Naotsugu Chinen

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 123 KB
• Volume: 102
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(98)00154-0

✦ Synopsis

A closed connected n-manifold N is called a codimension 2 fibrator (codimension 2 orientable fibrator, respectively) if each proper map p : M → 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 and let N be a closed n-manifold whose fundamental group is isomorphic to H 1 × H 2 , where H 1 is a group whose order is odd and H 2 is a finite direct product of cyclic groups of order 2 r . Let q 1 : N 1 → N be the covering associated with H 1 . The main purpose of this paper shows that if N 1 is a codimension 2 orientable fibrator, then N is a codimension 2 fibrator.