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Bocksteins and the nilpotent filtration on the cohomology of spaces

Gerald Gaudens

Geometry & Topology Monographs 11 (2007) 59–79

DOI: 10.2140/gtm.2007.11.59

arXiv: 0903.4909

Abstract

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.

Keywords

Steenrod operations, nilpotent modules, realization, Eilenberg–Moore spectral sequence

Mathematical Subject Classification

Primary: 55S10

Secondary: 55T20, 57T35

References
Publication

Received: 12 January 2005
Revised: 12 April 2005
Accepted: 21 April 2005
Published: 14 November 2007

Authors
Gerald Gaudens
Math Institut der Universität Bonn
Beringstr. 1
D-53115 Bonn
Germany