Browsing by Subject "Lens spaces"

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    KO-rings and J-groups of lens spaces
    (1998) Kırdar, Mehmet
    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.
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    KO-Rings of S2k+1/Zz2n
    (1998) Kirdar, M.
    For n ≥ 2, we describe the reduced real K-theory K̃O(Lk(2n)) of the standard lens space Lk(2n) in terms of generators and relations. In particular, we show that the K̃O-order of the Hopf bundle is 2n-1+2[k/2]. © 1998 Kluwer Academic Publishers.