Fadell, Edward; Husseini, Sufian On a theorem of Anosov on Nielsen numbers for nilmanifolds. (English) Zbl 0596.58035 Nonlinear functional analysis and its applications, Proc. NATO Adv. Study Inst., Maratea/Italy 1985, NATO ASI Ser., Ser. C 173, 47-53 (1986). [For the entire collection see Zbl 0583.00019.] The authors prove that for maps f of compact nilmanifolds the Nielsen number n(f) equals \(| L(f)|\), where L(f) is the Lefschetz-Hopf number [for definitions see R. F. Brown, The Lefschetz fixed point theorem (1971; Zbl 0216.196)]. Reviewer: Y.Kifer Cited in 2 ReviewsCited in 20 Documents MSC: 37D99 Dynamical systems with hyperbolic behavior 55M20 Fixed points and coincidences in algebraic topology 55N99 Homology and cohomology theories in algebraic topology Keywords:compact nilmanifolds; Nielsen number; Lefschetz-Hopf number; Lefschetz fixed point theorem Citations:Zbl 0583.00019; Zbl 0216.196 PDFBibTeX XML