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

  • Author / Creator
    Rahmati, Saeed
  • 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.

  • Subjects / Keywords
  • Graduation date
    2013-11
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3D50G586
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Peschke, George (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Cliff, Gerald (Mathematical and Statistical Sciences)
    • Bauer, Kristine (Mathematical and Statistical Sciences, University of Calgary)
    • Kuttler, Jochen (Mathematical and Statistical Sciences)
    • Troitsky, Vladimir (Mathematical and Statistical Sciences)
    • Sadofsky, Hal (Mathematical and Statistical Sciences, University of Oregon)