Projective resolutions over EI-categories
Author
Bahran, Cihan
Advisor
Yalçın, Ergün
Date
2012Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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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.