Bocksteins and the nilpotent filtration on the cohomology of spaces

Details Bocksteins and the nilpotent filtration on the cohomology of spaces Bocksteins and the nilpotent filtration on the cohomology of spaces

2009-03-27

arxiv.org/abs/0903.4909v1

Geom. Topol. Monogr. 11 (2007) 59-79

Mathematics

Algebraic Topology

This is the version published by Geometry & Topology Monographs on 14 November 2007

Scientific paper

10.2140/gtm.2007.11.59

N Kuhn has given several conjectures on the special features satisfied by the singular cohomology of topological spaces with coefficients in a finite prime field, as modules over the Steenrod algebra. The so-called realization conjecture was solved in special cases in [Ann. of Math. 141 (1995) 321-347] and in complete generality by L Schwartz [Invent. Math. 134 (1998) 211-227]. The more general strong realization conjecture has been settled at the prime 2, as a consequence of the work of L Schwartz [Algebr. Geom. Topol. 1 (2001) 519-548] and the subsequent work of F-X Dehon and the author [Algebr. Geom. Topol. 3 (2003) 399-433]. We are here interested in the even more general unbounded strong realization conjecture. We prove that it holds at the prime 2 for the class of spaces whose cohomology has a trivial Bockstein action in high degrees.

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