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Theory of Spectral Sequences of Exact Couples: Applications To Countably And Transfinitely Filtered Modules Open Access


Other title
Spectral Sequence, Exact Couple, Distribution Theorem, Transfinitely Filtered, Class of Modules, Comparison Theorems, Reverse Engineering
Type of item
Degree grantor
University of Alberta
Author or creator
Rahmati, Saeed
Supervisor and department
Peschke, George (Mathematical and Statistical Sciences)
Examining committee member and department
Kuttler, Jochen (Mathematical and Statistical Sciences)
Bauer, Kristine (Mathematical and Statistical Sciences, University of Calgary)
Troitsky, Vladimir (Mathematical and Statistical Sciences)
Cliff, Gerald (Mathematical and Statistical Sciences)
Sadofsky, Hal (Mathematical and Statistical Sciences, University of Oregon)
Department of Mathematical and Statistical Sciences
Date accepted
Graduation date
Doctor of Philosophy
Degree level
This thesis has two parts. In the first part we start from an arbitrary exact couple of R-modules and describe completely how the E-infinity terms of the associated spectral sequence relate to adjacent filtration stages of the universal (co-)augmenting objects of the exact couple. This advances earlier work, notably that of Boardman. In the second part we use these insights to develop a framework which permits spectral sequence methods to gain information about suitably transfinitely filtered objects. We offer several applications of this method: 1) We use Serre's idea of working relative to a class of modules while passing through the pages of the spectral sequence associated to an exact couple and we spell out conditions under which the filtration stages of countably or transfinitely filtered modules stay within such a class. 2) We extend Zeeman's comparison technique of spectral sequences to apply to a map between countably or transfinitely filtered modules. 3) Finally, we develop a general setting of reverse engineering information about finite pages in a spectral sequence from information about the universally filtered objects of the underlying exact couple.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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