Algebraic $K$-theory of poly-(finite or cyclic) groups

Algebraic X - Theory of Poly - ( Finite or Cylic ) Groups

The K-theory of the title is described in terms of the Ktheory of finite subgroups, as generalized sheaf homology of a quotient space. A corollary is that if G is torsion-free, then the Whitehead groups Wh t(ZG) vanish for all i. 1. The main result. Suppose that G is a poly-(finite or cyclic) group. Then there is a virtually connected and solvable Lie group L that contains G as a discrete cocom...

Algebraic Homotopy Theory, Groups, and K-Theory

A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in The Faculty of Graduate Studies Department of Mathematics. LetMk be the category of algebras over a unique factorization domain k, and let ind−Affk denote the category of pro-representable functions from Mk to the category E of sets. It is shown that ind−Affk is a closed model category in such...

Algebraic K-theory of Special Groups

Following the introduction of an algebraic K-theory of special groups in [6], generalizing Milnor’s mod 2 K-theory for fields, the aim of this paper is to compute the K-theory of Boolean algebras, inductive limits, finite products, extensions, SG-sums and (finitely) filtered Boolean powers of special groups. A parallel theme is the preservation by these constructions of property [SMC], an analo...

Algebraic K-theory of a Finite Field

The main goal of the present project is to give a sketch of the calculation of the algebraic K-theory of a finite field. Not all the details are developed, but several references are given where detailed proofs may be found. However, the main source of the project is D.J. Benson’s book on ”Representations and Cohomolgy: Cohomolgy of groups and modules” [4]. Section 1 is an introduction to princ...

Algebraic K-theory of Finite Fields