Related papers: A note on properly discontinuous actions
Motivated by the work of McCarthy and Papadopoulos for subgroups of mapping class groups, we construct domains of proper discontinuity in the compactified Outer space and in the projectivized space of geodesic currents for any "sufficiently…
We extend the notions of complete intersection dimension and lower complete intersection dimension to the category of complexes with finite homology and verify basic properties analogous to those holding for modules. We also discuss the…
The study of systems with sustained energy uptake and dissipation at the scale of the constituent particles is an area of central interest in nonequilibrium statistical physics. Identifying such systems as a distinct category -- Active…
We complete the classification of isometric cohomogeneity-one actions on all symmetric spaces of noncompact type up to orbit equivalence.
One approach to monitoring a dynamic system relies on decomposition of the system into weakly interacting subsystems. An earlier paper introduced a notion of weak interaction called separability, and showed that it leads to exact…
Brief development of the idea of the very important notion of continuity is given. Continuity is often confused with contiguity, "drawing the graph in one go," "no gaps," etc. The author argues in support of using correct notions of…
A finitely presented 1-ended group $G$ has {\it semistable fundamental group at infinity} if $G$ acts geometrically on a simply connected and locally compact ANR $Y$ having the property that any two proper rays in $Y$ are properly…
We investigate continuous transitive actions of semitopological groups on spaces, as well as separately continuous transitive actions of topological groups.
Our aim is to find some new links between linear (circular) orderability of groups and topological dynamics. We suggest natural analogs of the concept of algebraic orderability for topological groups involving order-preserving actions on…
We show that if a (locally compact) group $G$ acts properly on a locally compact $\sigma$-compact space $X$ then there is a family of $G$-invariant proper continuous finite-valued pseudometrics which induces the topology of $X$. If $X$ is…
This is a continuation of the paper (quant-ph/0009012). In this letter we extend coherent operators and study some basic properties (the disentangling formula, resolution of unity, commutation relation, etc). We also propose a perspective…
Various concerns suggest looking for internal co-categories in categories with strong logical structure. It turns out that in any coherent category, all co-categories are co-equivalence relations.
Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete Riemannian manifold of non-positive sectional curvature or a locally finite tree). Isometric actions of G on M are (by definition) points in the…
We study the general problem of the behaviour of the continuum function in the presence of non-supercompact strongly compact cardinals.
We consider the notion of improved and perfect actions within Regge calculus. These actions are constructed in such a way that they - although being defined on a triangulation - reproduce the continuum dynamics exactly, and therefore…
We consider the deformation of a discontinuous group acting on the Euclidean space by affine transformations. A distinguished feature here is that even a `small' deformation of a discrete subgroup may destroy proper discontinuity of its…
We introduce some equivalent notions of homomorphisms between quantum groups that behave well with respect to duality of quantum groups. Our equivalent definitions are based on bicharacters, coactions, and universal quantum groups,…
For a metric space $(A,d)$, and a set $\Sigma$ of equations, some quantities are introduced that measure the size of discontinuities that must occur in operations satisfying $\Sigma$ (identically) on $A$. We are able to evaluate these…
In this paper the metric on the set of mixing actions of a countable infinite group is introduced so that the corresponding space is complete and separable. Keywords and phrases. Monotilable group, measure preserving transformations, mixing…
A global action is an algebraic analogue of a topological space. It consists of group actions $G_\alpha\curvearrowright X_\alpha$, $(\alpha\in\Phi)$, which fulfill a certain compatibility condition. We investigate the homotopy theory of…