Lefschetz and Nielsen coincidence numbers on nilmanifolds and solvmanifolds, II

✍ Scribed by Christopher K. McCord

• Book ID: 104295113
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 784 KB
• Volume: 75
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(96)00081-8

✦ Synopsis

McCord (1991)

claimed that Nielsen coincidence numbers and Lefschetz coincidence numbers are related by the inequality N(f,g) 2 IL(f,g)l f or all maps f, g : S1 --t SZ between compact orientable solvmanifolds of the same dimension. It was further claimed that N(f, g) = lL(f, g)l when ,572 is a nilmanifold. A mistake in that paper has been discovered. In this paper, that mistake is partially repaired. A new proof of the equality N(f, g) = ]~5(f, g)l for nilmanifolds is given, and a variety of conditions for maps on orientable solvmanifolds are established which imply the inequality N(f, 9) 2 lL(f, g)l. H owever, it still remains open whether N(f, g) 2 IL(f, g)l for all maps between orientable solvmanifolds.