dc.contributor.advisor Yalçın, Ergün dc.contributor.author Bahran, Cihan dc.date.accessioned 2016-01-08T18:19:04Z dc.date.available 2016-01-08T18:19:04Z dc.date.issued 2012 dc.identifier.uri http://hdl.handle.net/11693/15472 dc.description Ankara : The Department of Mathematics and the Graduate School of Engineering and Science of Bilkent University, 2012. en_US dc.description Thesis (Master's) -- Bilkent University, 2012. en_US dc.description Includes bibliographical references leaves 101-102. en_US dc.description.abstract Representations of EI-categories occur naturally in algebraic K-theory and algebraic en_US 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. dc.description.statementofresponsibility Bahran, Cihan en_US dc.format.extent vii, 102 leaves en_US dc.language.iso English en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.subject EI-categories en_US dc.subject projective dimension en_US dc.subject constant functor en_US dc.subject orbit categories en_US dc.subject Rim’s theorem en_US dc.subject.lcc QA169 .B34 2012 en_US dc.subject.lcsh Categories (Mathematics) en_US dc.subject.lcsh Functor theory. en_US dc.subject.lcsh Algebraic functions. en_US dc.subject.lcsh Projective spaces. en_US dc.subject.lcsh K-theory. en_US dc.title Projective resolutions over EI-categories en_US dc.type Thesis en_US dc.department Department of Mathematics en_US dc.publisher Bilkent University en_US dc.description.degree M.S. en_US
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