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      • Theses - Department of Mathematics
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      Projective resolutions over EI-categories

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      Author
      Bahran, Cihan
      Advisor
      Yalçın, Ergün
      Date
      2012
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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      Abstract
      Representations 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.
      Keywords
      EI-categories
      projective dimension
      constant functor
      orbit categories
      Rim’s theorem
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      http://hdl.handle.net/11693/15472
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      • Dept. of Mathematics - Master's degree 125
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