An unstable Adams spectral sequence based on a generalized homology theory.
Item
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Title
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An unstable Adams spectral sequence based on a generalized homology theory.
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Identifier
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AAI9908330
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identifier
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9908330
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Creator
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Kargl, Roland.
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Contributor
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Adviser: Robert Thompson
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Date
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1998
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics
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Abstract
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An unstable Adams spectral sequence based on a non-connective homology theory is constructed and its {dollar}E\sb2{dollar}-term is described. The involved homology theory arises from an arbitrary unital ring spectrum E which gives rise to a triple on the homotopy category of spaces. This triple defines, following techniques by Bousfield and Kan, a spectral sequence whose {dollar}E\sb2{dollar}-term can be described using cosimplicial methods.;After imposing further restrictions on E, namely (1) E is a homotopy commutative, flat CW ring spectrum; (2) for each {dollar}n\ge0,\ E\sb{lcub}\*{rcub}{dollar}(E{dollar}\rm\sb{lcub}n{rcub}){dollar} is a free {dollar}E\sb{lcub}\*{rcub}{dollar}-module, where E is represented by an {dollar}\Omega{dollar}-spectrum {dollar}\{lcub}{dollar}E{dollar}\rm\sb{lcub}n{rcub}\{rcub},{dollar} the {dollar}E\sb2{dollar}-term can be identified--at least for spaces with free E-homolog--as an unstable Ext-term in the category of G-coalgebras. G is the functor of a cotriple on the category of free {dollar}E\sb{lcub}\*{rcub}{dollar}-modules which, by analogy, can be thought of computing the homology of a generalized Eilenberg-MacLane space. For suitable E and spaces X this {dollar}E\sb2{dollar}-term can be interpreted as an Ext-term in an abelian category and computed using the cobar complex.;The main result of this work deals with the starting point of this computation in the case of {dollar}E=E(n),{dollar} the Johnson-Wilson spectra. An unstable change of rings isomorphism is provided that relates the Ext-terms based on E(n)-theory to those in BP-theory for a certain class of modules.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
