Related papers: Asymptotic transfer maps in parametrized K-theory

We construct a new type of S-matrix in quantum field theory using the general boundary formulation. In contrast to the usual S-matrix the space of free asymptotic states is located at spatial rather than at temporal infinity. Hence, the new…

In this article we study a coarse version of the $K$-theoretic Farrell--Jones conjecture we call coarse or bounded isomorphism conjecture. Using controlled category theory we are able to translate this conjecture for asymptotically faithful…

Structural properties of large random maps and lambda-terms may be gleaned by studying the limit distributions of various parameters of interest. In our work we focus on restricted classes of maps and their counterparts in the…

In nature, one observes that a K-theory of an object is defined in two steps. First a "structured" category is associated to the object. Second, a K-theory machine is applied to the latter category to produce an infinite loop space. We…

In this paper we show that the Farrell-Jones isomorphism conjectures are inherited in group extensions for assembly maps in algebraic $K$-theory and $L$-theory with twisted coefficients.

Index maps taking values in the $K$-theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. The framework of geometric $K$-homology is used in a…

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…

We establish some basic theorems in dimension theory and absolute extensor theory in the coarse category of metric spaces. Some of the statements in this category can be translated in general topology language by applying the Higson corona…

The asymptotic expansion method is generalized from the periodic setting to stationary ergodic stochastic geometries. This will demonstrate that results from periodic asymptotic expansion also apply to non-periodic structures of a certain…

We construct quantum K-invariants in non-archimedean analytic geometry. Contrary to the classical approach in algebraic geometry via perfect obstruction theory, we build on our previous works on the foundations of derived non-archimedean…

In this article, we consider regular projective arithmetic schemes in the context of Arakelov geometry, any of which is endowed with an action of the diagonalisable group scheme associated to a finite cyclic group and with an equivariant…

These lectures introduce the notion of asymptotic observables, which are classes of measurable quantities predicted by quantum field theory. In gapped theories with trivial infrared dynamics, these include scattering amplitudes, expectation…

We give rigorous foundations for parametrized homotopy theory in this monograph. After preliminaries on point-set topology, base change functors, and proper actions of non-compact Lie groups, we develop the homotopy theory of equivariant…

We study the asymptotics of iterates of the transfer operator for non-uniformly hyperbolic $\alpha$-Farey maps. We provide a family of observables which are Riemann integrable, locally constant and of bounded variation, and for which the…

In this paper, we present a new method via the transfer matrix approach to obtain asymptotic formulae of orthogonal polynomials with asymptotically identical coefficients of bounded variation. We make use of the hyperbolicity of the…

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…

The paper is devoted to the problem when a map from some closed connected manifold to an aspherical closed manifold approximately fibers, i.e., is homotopic to Manifold Approximate Fibration. We define obstructions in algebraic K-theory.…

For a countable discrete group $G$, we construct a new and concrete model for the equivariant topological $K$-homology theory of $G$, which is defined for all $G$-actions, not just for proper $G$-actions. The construction of our model…

We establish various results on the large level limit of projective quantum representations of surface mapping class groups obtained by quantizing moduli spaces of flat SU(n)-bundle. Working with the metaplectic correction, we proved that…

The work discusses equivariant asymptotic dimension (also known as "wide equivariant covers", "$N$-$\mathcal F$-amenability" or "amenability dimension", and "$d$-BLR condition") and its generalisation, transfer reducibility, which are…