Algebraic K -theory over the infinite dihedral group: a controlled topology approach

Algebraic K-theory over the infinite dihedral group: a controlled topology approach

We use controlled topology applied to the action of the infinite dihedral group on a partially compactified plane and deduce two consequences for algebraic K-theory. The first is that the family in the K-theoretic Farrell–Jones conjecture can be reduced to only those virtually cyclic groups that admit a surjection with finite kernel onto a cyclic group. The second is that the Waldhausen Nil gro...

Non-commutative convolutional codes over the infinite dihedral group

Classic convolutional codes are defined as the convolution of a message and a transfer function over Z. In this paper, we study convolutional codes over the infinite dihedral group D∞. The goal of this study is to design convolutional codes with good and interesting properties and intended to be more resistant to code recognition. Convolution of two functions on D∞ corresponds to the product of...

Algebraic $ $ K $ $ K - theory of the infinite place

We show that the algebraic K -theory of generalized archimedean valuation rings occurring in Durov’s compactification of the spectrum of a number ring is given by stable homotopy groups of certain classifying spaces.We also show that the “residue field at infinity” is badly behaved from a K -theoretic point of view.

Controlled Algebraic K-Theory of Integral Group Ring of ...

We calculate the lower Controlled Algebraic K-theory of any nitely generated innnite subgroup of SL(3; Z), the group of 3 3 integral matrices of determinant 1.ally (innnite) cyclic groups.

A1-Algebraic topology over a eld