The eta invariant and the Gromov-Lawson conjecture for elementary Abelian groups of odd order

✍ Scribed by Boris Botvinnik; Peter B. Gilkey

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 752 KB
• Volume: 80
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(97)00003-5

✦ Synopsis

Let M be a compact connected spin manifold of dimension m > 5. Assume the fundamental group of M is an elementary Abelian p group of rank k where p is an odd prime. If k = 2 and m is arbitrary or if k = 3 and m is odd, we use the eta invariant to show that M admits a metric of positive scalar curvature if and only if the i-roof genus of nil vanishes. This establishes the Gromov-Lawson conjecture for these cases.