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      • Theses - Department of Mathematics
      • Dept. of Mathematics - Ph.D. / Sc.D.
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      KO-rings and J-groups of lens spaces

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      Author(s)
      Kırdar, Mehmet
      Advisor
      Dibağ, İbrahim
      Date
      1998
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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      Abstract
      In this thesis, we make the explicit computation of the real A'-theory of lens spaces and making use of these results and Adams conjecture, we describe their .7-groups in terms of generators and relations. These computations give nice by-products on some geometrical problems related to lens spaces. We show that J-groups of lens spaces approximate localized J-groups of complex projective spaces. We also make connections of the J-cornputations with the classical cross-section problem and the .James numbers conjecture. Many difficult geometric problems remain open. The results are related to some arithmetic on representations of cyclic groups o\er fields and the Atiyah-Segal isomormhisrn. Eventually, we are interested in representations over rings, in connection with Algebraic K-theory. This turns out to lie a very non-trivial arithmetic problem related to number theory.
      Keywords
      Topological K-Theory
      Lens spaces
      Representations of cyclic groups
      J-groups
      Im(J)-theory
      Algebraic K-theory
      Permalink
      http://hdl.handle.net/11693/18554
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      • Dept. of Mathematics - Ph.D. / Sc.D. 49
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