The Bousfield -Kan spectral sequence for Morava K -theory.
Item
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Title
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The Bousfield -Kan spectral sequence for Morava K -theory.
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Identifier
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AAI3144109
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identifier
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3144109
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Creator
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La Luz, Jose.
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Contributor
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Adviser: Martin Bendersky
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Date
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2004
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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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Given a homology theory E, we can construct the Bousfield-Kan spectral sequence. Even though one can set this spectral sequence with great generality, the E2-term turns out to be an Ext group in some non-abelian category. In practical terms this description limits our ability to make computations. If we require E to be a Landweber exact homology theory and with some mild assumptions on the space X, then we can relate the E 2-term to an Ext group in an abelian category, which in turn can be calculated as the homology of some subcomplex of the stable cobar complex. Although Morava's K theories do not satisfy this property, there is a spectral sequence converging to the E2-term of the BK spectral sequence. The input to this spectral sequence can be calculated again as the homology of some unstable cobar complex. In the case of K(1) and for any space X such that K(1) *(X) is cofree as a coalgebra, this spectral sequence collapses and we get a complete description of the E 2-term of the BK spectral sequence for X. As observed by N. Kuhn, this turns out to be isomorphic to the stable E 2-term. Using this we determine all the differentials and thus prove convergence of the spectral sequence to the unstable K(1)-completion of the odd spheres.
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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.
