Related papers: Free product actions and their applications
We show that any free product of two countable groups, one of them being infinite, admits a faithful and homogeneous action on the Random Graph. We also show that a large class of HNN extensions or free products, amalgamated over a finite…
In various classes of infinite groups, we identify groups that are presentable by products, i.e. groups having finite index subgroups which are quotients of products of two commuting infinite subgroups. The classes we discuss here include…
The aim of this paper is to provide a general overview of the product operators introduced in the literature as a tool to enhance the analysis accuracy in the Abstract Interpretation framework. In particular we focus on the Cartesian and…
We study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. We develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint…
We develop a refinement of Whitehead's algorithm for primitive words in a free group. We generalize to subgroups, establishing a strengthened version of Whitehead's algorithm for free factors. We make use of these refinements in proving new…
The aim of this paper is to investigate whether the class of automaton semigroups is closed under certain semigroup constructions. We prove that the free product of two automaton semigroups that contain left identities is again an automaton…
We prove that certain free products of factors of type ${\rm I}$ and other von Neumann algebras with respect to nontracial, almost periodic states are almost periodic free Araki-Woods factors. In particular, they have the free absorption…
In this article we introduce powerful tools and techniques from invariant theory to free analysis. This enables us to study free maps with involution. These maps are free noncommutative analogs of real analytic functions of several…
This paper is devoted to the investigation of the property of order separability for free products of groups.
We study the behaviour of infinitesimal deformation functors of local group actions with regard to passing to subgroups and quotient groups. Inspired by the cohomological information, we conjecture the existence of a decomposition of a…
We investigate proposals of how the form factor approach to compute correlation functions at zero temperature can be extended to finite temperature. For the two-point correlation function we conclude that the suggestion to use the usual…
In this note we study the freeness of the module of derivations on all moduli of the $X_3$ arrangement with multiplicities. We use homological techniques stemming from work of Yuzvinsky, Brandt, and Terao which have recently been developed…
We study some aspects of divisionally free arrangements which were recently introduced by Abe. Crucially, Terao's conjecture on the combinatorial nature of freeness holds within this class. We show that while it is compatible with products,…
We provide an elementary proof that subgroups of free groups are free via group actions.
We show how several useful properties of Ind-constructions in $\infty$-categories extend to arbitrary free colimit completion constructions.
This is a note of the author's lectures at "Advanced courses in Foliation" in the research program "Foliation", which was held at the Centre de Recerca Mathematica in the May of 2010. In this note, we discuss about the relationship between…
We construct an explicit combinatorial model of the functor which adds right adjoints to the morphisms of an $\infty$-category, and we speculate on possible extensions to higher dimensions.
Let $G$ be a group which admits the structure of an iterated semidirect product of finitely generated free groups. We construct a finite, free resolution of the integers over the group ring of $G$. This resolution is used to define…
In this chapter we review some recent results on the dynamics of price formation in financial markets and its relations with the efficient market hypothesis. Specifically, we present the limit order book mechanism for markets and we…
We examine free orientation-reversing group actions on orientable handlebodies, and free actions on nonorientable handlebodies. A classification theorem is obtained, giving the equivalence classes and weak equivalence classes of free…