模2幂零上同调的3- polyGEM
Un 3-polyGEM de cohomologie modulo 2 nilpotente
摘要：
1983年，C. McGiant和J. Neisendorfer在J. P. Serre的著名论文（1953）。1985年，J. Lannes和L.施瓦茨。从那时起，人们考虑了一个更一般的猜想：如果任何1-连通polyGEM的约化模2上同调是有限型的并且不是平凡的，那么它至少包含一个无限高的元素，即，非幂零这个猜想在几种特殊情况下得到了验证，更确切地说，Y。Felix，S. Halperin，J.- M. Lemaire和J. - C. Thomas于1987年由J. Lannes和L. Schwartz在1988年和J. Grodal在1996年提出的。在本文中，我们构造了一个例子，这个猜想失败。
英文摘要：
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.
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