8 citations · 23 across the 15 of their papers we have counts for
9 papers · 1 filter
Asymptotic transfer maps in parametrized K-theory
Gunnar Carlsson, Boris Goldfarb
We define asymptotic transfers in bounded K-theory together with a context where this can be done in great generality. Controlled algebra plays a central role in many advances in g…
Colimit theorems for coarse coherence with applications
Boris Goldfarb, Jonathan L. Grossman
We establish two versions of a central theorem, the Family Colimit Theorem, for the coarse coherence property of metric spaces. This is a coarse geometric property and so is well-d…
Excision in equivariant fibred G-theory
Gunnar Carlsson, Boris Goldfarb
This paper provides a generalization of excision theorems in controlled algebra in the context of equivariant G-theory with fibred control and families of bounded actions. It also…
Bounded G-theory with fibred control
Gunnar Carlsson, Boris Goldfarb
We use filtered modules over a Noetherian ring and fibred bounded control on homomorphisms to construct a new kind of controlled algebra with applications in geometric topology. Th…
Coarse coherence of metric spaces and groups and its permanence properties
Boris Goldfarb, Jonathan L. Grossman
We introduce properties of metric spaces and, specifically, finitely generated groups with word metrics which we call coarse coherence and coarse regular coherence. They are geomet…
On Modules over Infinite Group Rings
Gunnar Carlsson, Boris Goldfarb
Let be a commutative ring and be an infinite discrete group. The algebraic -theory of the group ring is an important object of computation in geometric topology a…
Controlled algebraic G-theory, II
Boris Goldfarb, Timothy K. Lance
There are two established ways to introduce geometric control in the category of free modules---the bounded control and the continuous control at infinity. Both types of control ca…
K-theory of geometric modules with fibred control
Gunnar Carlsson, Boris Goldfarb
Controlled algebra plays a central role in many recent advances in geometric topology. This paper studies the iteration construction that was present from the very origins of the t…
Controlled algebraic G-theory, I
Gunnar Carlsson, Boris Goldfarb
This paper extends the notion of geometric control in algebraic K-theory from additive categories with split exact sequences to other exact structures. In particular, we construct…