Browsing by Subject "K-theory."
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Open Access KO-rings and J-groups of lens spaces(Bilkent University, 1998) Kırdar, MehmetIn 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.Item Open Access Projective resolutions over EI-categories(Bilkent University, 2012) Bahran, CihanRepresentations of EI-categories occur naturally in algebraic K-theory and algebraic topology (see [4], [10], [12]). In this thesis, we study EI-category representations with finite projective dimension. We apply this general theory to orbit categories of finite groups and prove Rim’s theorem for the orbit category (Theorem B in [5]). It follows from this theorem that, for a fixed prime p, the constant functor over the orbit category of a finite group G with respect to the family of p-subgroups and with coefficients in Z(p) has finite projective dimension, which we denote by pd(G, p). In this thesis, we calculate pd(S4, 2) and pd(S5, 2) explicitly, which are among the first nontrivial cases. We also prove that the constant functor over the orbit category of all subgroups with prime power order and with integral coefficients never has a finite projective resolution unless G itself has prime power order.