Related papers: Displacement techniques in bounded cohomology
Commutativity gadgets provide a technique for lifting classical reductions between constraint satisfaction problems to quantum-sound reductions between the corresponding nonlocal games. We develop a general framework for commutativity…
We use cross ratios to describe second real continuous bounded cohomology for locally compact topological groups. We also derive a rigidity result for cocycles with values in the isometry group of a proper hyperbolic geodesic metric space.
It is shown that if a metric space exhibits certain finiteness and tree-like properties, then elements of its group of bounded displacement which are infinitely divisible are also torsion. This extends a result of N. M. Suchkov, A. A.…
We prove that the groups of orientation-preserving homeomorphisms and diffeomorphisms of $\mathbb{R}^n$ are boundedly acyclic, in all regularities. This is the first full computation of the bounded cohomology of a transformation group that…
We report on the following highlights from among the many discoveries made in Noncommutative Geometry since year 2000: 1) The interplay of the geometry with the modular theory for noncommutative tori, 2) Advances on the Baum-Connes…
This paper presents a gentle introduction to cohomology vanishing theorems, largely based on the paper work of Hongshan Li. It offers an insightful exploration of unitary local systems on complex manifolds, particularly focusing on their…
In this paper, we study a connection between disintegration of measures and geometric properties of probability spaces. We prove a disintegration theorem, addressing disintegration from the perspective of an optimal transport problem. We…
It is known that pure row contractions with one-dimensional defect spaces can be classified up to unitary equivalence by compressions of the standard $d$-shift acting on the full Fock space. Upon settling for a softer relation than unitary…
A characteristic property of cohomology with compact support is the long exact sequence that connects the compactly supported cohomology groups of a space, an open subspace and its complement. Given an arbitrary cohomology theory of…
A generalization of Connes-Thom isomorphism is given for stable, homotopy invariant, and split exact functors on separable $C^*$-algebras. As examples of these functors, we concentrate on asymptotic and local cyclic cohomology and the…
Given a graded-commutative ring acting centrally on a triangulated category, our main result shows that if cohomology of a pair of objects of the triangulated category is finitely generated over the ring acting centrally, then the…
We provide new vanishing and glueing results for relative simplicial volume, following up on two current themes in bounded cohomology: The passage from amenable groups to boundedly acyclic groups and the use of equivariant topology. More…
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…
A construction of conservation laws for $\sigma$-models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing the ordinary calculus of differential forms with other…
The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase…
This survey gives a unified treatment of topics from Abelian and non-Abelian Nielsen Theory integrated with the semiconjugacy theorems of Franks and Handel. The main focus is to develop an analog of the rotation set that is valid when the…
We prove the vanishing of certain low degree cohomologies of some induced representations. As an application, we determine certain low degree cohomologies of congruence groups.
We present a new criterion, based on commutator methods, for the strong mixing property of unitary representations of topological groups equipped with a proper length function. Our result generalises and unifies recent results on the strong…
Commuting and noncommuting space-time coordinates in a class of deformed special relativity theories are investigated. Their momentum space representation, transformation behaviour, space-time algebra, invariants and the corresponding field…
This paper analyzes the second cohomology group of a linear cycle set with coefficients in an abelian group I, for linear cycle sets with commutative adjoint operation, focusing on the finite abelian case. It aims to classify extensions of…