## Projective resolutions over EI-categories

##### Author

Bahran, Cihan

##### Advisor

Yalçın, Ergün

##### Date

2012##### Publisher

Bilkent University

##### Language

English

##### Type

Thesis##### Item Usage Stats

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Show full item record##### 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-categoriesprojective dimension

constant functor

orbit categories

Rim’s theorem

QA169 .B34 2012

Categories (Mathematics)

Functor theory.

Algebraic functions.

Projective spaces.

K-theory.