2003/06/17 by Jiang Hua, Jiang Dong Hua, Hua, Jiang Dong
Mathematics · #Algebraic Geometry and Number Theory #math.AT #msc:55N99 #msc:55P20
paper · pdf · doi:10.48550/arxiv.math/0306253
accepted in les Annales de l'Institut Fourier
arxiv created 2004/04/29 · arxiv updated 2009/11/30
In 1983, C. McGibbon and J. Neisendorfer have given a proof for one conjecture in J.-P. Serre's famous paper (1953). In 1985, another proof was given by J. Lannes and L. Schwartz. Since then, one considers a more general conjecture: if the reduced mod 2 cohomology of any 1-connected polyGEM is of finite type and is not trivial, then it contains at least one element of infinite height, i.e., non nilpotent. This conjecture has been verified in several special situations, more precisely, by Y. Felix, S. Halperin, J.-M. Lemaire and J.-C. Thomas in 1987, by J. Lannes and L. Schwartz in 1988, and by J. Grodal in 1996. In this note, we construct an example, for which this conjecture fails.