I–adic towers in topology

Wüthrich, Samuel¹

¹Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, United Kingdom

Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1589-1635

Résumé

A large variety of cohomology theories is derived from complex cobordism MU∗(−) by localizing with respect to certain elements or by killing regular sequences in MU∗. We study the relationship between certain pairs of such theories which differ by a regular sequence, by constructing topological analogues of algebraic I–adic towers. These give rise to Higher Bockstein spectral sequences, which turn out to be Adams spectral sequences in an appropriate sense. Particular attention is paid to the case of completed Johnson–Wilson theory Ê(n) and Morava K–theory K(n) for a given prime p.

Détail

DOI : 10.2140/agt.2005.5.1589

Keywords: structured ring spectra, Adams resolution, Adams spectral sequence, Bockstein operation, complex cobordism, Morava $K$–theory, Bousfield localization, stable homotopy theory.

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