Related papers: Displacement techniques in bounded cohomology
Some criteria for graded local cohomology to commute with coarsening functors are proven, and an example is given where graded local cohomology does not commute with coarsening.
In this article we study cohomology of a group with coefficients in representations on Banach spaces and its stability under deformations. We show that small, metric deformations of the representation preserve vanishing of cohomology. As…
We prove some injectivity, torsion-free, and vanishing theorems for simple normal crossing pairs. Our results heavily depend on the theory of mixed Hodge structures on compact support cohomology groups. We also treat several basic…
We study some basic properties of sofic-Dyck shifts and finite-type-Dyck shifts. We prove that the class of sofic-Dyck shifts is stable under proper conjugacies. We prove a Decomposition Theorem of a proper conjugacy between edge-Dyck…
This is the second of two papers in which we investigate the properties of displacement functions of automorphisms of free groups (more generally, free products) on the Culler-Vogtmann Outer space $CV_n$ and its simplicial bordification. We…
As an algebraic study of differential equations, differential algebras have been studied for a century and and become an important area of mathematics. In recent years the area has been expended to the noncommutative associative and Lie…
The Homeomorphic Embedding relation has been amply used for defining termination criteria of symbolic methods for program analysis, transformation, and verification. However, homeomorphic embedding has never been investigated in the context…
In this PhD thesis we will discuss some aspects in Commutative Algebra which have interactions with Algebraic Geometry, Representation Theory and Combinatorics. In particular, in the first chapter we will focus on understanding when certain…
In the paper ``Weil transfer of algebraic cycles'', published by the second author in Indagationes Mathematicae about 25 years ago, a Weil transfer map for Chow groups of smooth algebraic varieties has been constructed and its basic…
We show that symmetry in the vanishing of cohomology holds for graded modules over quantum complete intersections. Moreover, symmetry holds for all modules if the algebra is symmetric.
We establish a "second vanishing theorem" for local cohomology modules over regular rings of unramified mixed characteristic, which relates the connectedness of the spectrum of a ring with the vanishing of local cohomology. Applying this,…
We introduce separability properties corresponding to generalized versions of the conjugacy, twisted conjugacy, Brinkmann and Brinkmann's conjugacy problems and how they relate when finite and cyclic extensions of groups are taken. In…
This paper studies the sliced nearby cycle functor and its commutation with duality. Over a Henselian discrete valuation ring, we show that this commutation holds, confirming a prediction of Deligne. As an application we give a new proof of…
We formulate a systematic construction of commuting quantum traces for reflection algebras. This is achieved by introducing two sets of generalized reflection equations with associated consistent fusion procedures. Products of their…
We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…
We provide a version of Quillen's homological stability criterion for continuous bounded cohomology. This criterion is exploited in the companion paper (arXiv:2201.03879) in order to derive new bounded cohomological stability results for…
Consistent tensor products on auxiliary spaces, hereafter denoted "fusion procedures", are defined for general quadratic algebras, non-dynamical and dynamical, inspired by results on reflection algebras. Applications of these procedures…
Commutative K-theory, a cohomology theory built from spaces of commuting matrices, has been explored in recent work of Adem, G\'{o}mez, Gritschacher, Lind, and Tillman. In this article, we use unstable methods to construct explicit…
Topological defects play an important role in physics of elastic media and liquid crystals. Their kinematics is determined by constraints of topological origin. An example is the glide motion of dislocations which has been extensively…
This is the first of two papers in which we investigate the properties of the displacement functions of automorphisms of free groups (more generally, free products) on Culler-Vogtmann Outer space and its simplicial bordification - the free…