Le complexe de chaı̂nes d'un G-complexe simplicial acyclique

✍ Scribed by Serge Bouc

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 155 KB
• Volume: 220
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.7983

✦ Synopsis

Let G be a finite group. The main result of this note shows that the reduced chain complex of an acyclic finite dimensional simplicial G-complex is a split acyclic complex of G-modules.

The proof requires the extension of well known results on finitely generated ppermutation modules to arbitrary p-permutation modules. The key is a theorem stating that a bounded complex of p-permutation modules is split acyclic if and only if all its Brauer quotients are acyclic.