Related papers: Bounded G-theory with fibred control

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 theory but started being exploited only recently. We develop…

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 exact categories of modules over a Noetherian ring filtered…

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 states and proves several characteristic features of this…

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 can be generalized to arbitrary modules over a noetherian ring…

We develop aspects of geometric control theory on Lie groups G which may be infinite dimensional, and on smooth G-manifolds M modelled on locally convex spaces. As a tool, we discuss existence and uniqueness questions for differential…

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 geometric topology, including recent work on Novikov, Borel,…

We develop a generalization of quantitative $K$-theory, which we call controlled $K$-theory. It is powerful enough to study the $K$-theory of crossed product of $C^*$-algebras by action of \'etale groupoids and discrete quantum groups. In…

This paper provides a full controlled version of algebraic $K$-theory. This includes a rich array of assembly maps; the controlled assembly isomorphism theorem identifying the controlled group with homology; and the stability theorem…

We develop an epsilon-controlled algebraic L-theory, extending our earlier work on epsilon-controlled algebraic K-theory. The controlled L-theory is very close to being a generalized homology theory; we study analogues of the homology exact…

We prove new quantitative bounds on the additive structure of sets obeying an $L^3$ 'control' assumption, which arises naturally in several questions within additive combinatorics. This has a number of applications - in particular we…

We develop a version of controlled algebra for simplicial rings. This generalizes the methods which lead to successful proofs of the algebraic K- theory isomorphism conjecture (Farrell-Jones Conjecture) for a large class of groups. This is…

In this paper, we present a geometric approach for computing controlled invariant sets for hybrid control systems. While the problem is well studied in the ellipsoidal case, this family is quite conservative for constrained or switched…

A geometric setup for control theory is presented. The argument is developed through the study of the extremals of action functionals defined on piecewise differentiable curves, in the presence of differentiable non-holonomic constraints.…

A unifying framework for the control of quantum systems with non-Abelian holonomy is presented. It is shown that, from a control theoretic point of view, holonomic quantum computation can be treated as a control system evolving on a…

There are a number of (co-)homology theories on coarse spaces. Controlled operator K-theory is by far the most popular one of them. Our approach is geometric. We study when does the Roe-algebra of a space restrict to a subspace. Then we…

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…

Let T be the unit circle in the complex plane C. This paper proves the existence of analytic structure in a compact subset K of T X C^n, where K has so-called "lineally convex" or "hypoconvex" fibers over T. It also addresses a related…

We prove a squeezing/stability theorem for delta-epsilon controlled L-groups when the control map is a fibration on a finite polyhedron. A relation with boundedly-controlled L-groups is also discussed.

We extend the second Noether theorem to optimal control problems which are invariant under symmetries depending upon k arbitrary functions of the independent variable and their derivatives up to some order m. As far as we consider a…

Higher Homotopy van Kampen Theorems allow the computation as colimits of certain homotopical invariants of glued spaces. One corollary is to describe homotopical excision in critical dimensions in terms of induced modules and crossed…