Colimits in the proper homotopy category.
Item
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Title
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Colimits in the proper homotopy category.
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Identifier
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AAI9315491
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identifier
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9315491
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Creator
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Misir, Dasarat Totaram.
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Contributor
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Adviser: Alex Heller
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Date
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1993
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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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We study the proper homotopy category of the Category {dollar}{lcub}\cal L{rcub}{dollar} of locally finite CW complexes. An object in {dollar}{lcub}\cal L{rcub}{dollar} can be considered as being bi-filtered. This leads us to consider functor categories {dollar}C\sp{lcub}\cal J{rcub}{dollar}, where C is a category of CW complexes and {dollar}{lcub}\cal J{rcub}{dollar} a small category that encodes the bifiltered character of an object in {dollar}{lcub}\cal L{rcub}{dollar}. We are able to show that {dollar}C\sp{lcub}\cal J{rcub}{dollar} has enough structure to enable us to calculate left homotopy Kan extensions in appropriate fraction categories of {dollar}C\sp{lcub}\cal J{rcub}{dollar}. Also, we show that the proper homotopy category of {dollar}{lcub}\cal L{rcub}{dollar} is equivalent to a fraction category of {dollar}K\sp{lcub}W{rcub}{dollar}, where K is the category of finite CW complexes and cellular maps, and W an appropriate subcategory of {dollar}{lcub}\cal J{rcub}{dollar}.;These results enable us to show that certain constructions in the ordinary homotopy category which are homotopy colimits, when considered in the proper homotopy category, turnout to be left homotopy Kan extensions. Further, the Milnor's classifying space construction lifts to the proper homotopy category when the group is finite.
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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.
