Finite groups and approximate fibrations

✍ Scribed by Naotsugu Chinen

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 277 KB
• Volume: 102
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(98)00142-4

✦ Synopsis

A closed connected n-manifold N is called a codimension-2 fibrator (codimension-2 orientable fibrator, respectively) if every 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. The aim of this paper is to prove the following three statements:

If N is a closed manifold whose fundamental group is isomorphic to a finite product of Z 2 r 's for some r, then N is a codimension-2 fibrator.

(iii) Let N be a hopfian n-manifold with

The method used in (i) and (ii) induces the following: If a codimension-2 PL fibrator N satisfies that both π 1 (N) and π k-1 (N) are finite and that π i (N) = 0 for 2 i k -2, then N is a codimension-k PL fibrator.