We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...
Dynamical systems are topologically equivalent when their orbits can be mapped onto each other via a homeomorphic change of coordinates. We will show that in general, closed-loop systems resulting from Linear Quadratic Optimal Control problems are all topo ...
We show that the finitely generated simple left orderable groups G(rho) constructed by the first two authors in Hyde and Lodha [Finitely generated infinite simple groups of homeomorphisms of the real line. Invent. Math. (2019), doi:10.1007/s00222-01900880- ...
We show that for a large class C of finitely generated groups of orientation preserving homeomorphisms of the real line, the following holds: Given a group G of rank k in C, there is a sequence of k-markings (G,S-n), n is an element of N whose limit in the ...
We study actions of groups by orientation preserving homeomorphisms on R (or an interval) that are minimal, have solvable germs at +/-infinity and contain a pair of elements of a certain dynamical type. We call such actions coherent. We establish that such ...
Let G be the homeomorphism group of a dendrite. We study the normal subgroups of G. For instance, there are uncountably many nonisomorphic such groups G that are simple groups. Moreover, these groups can be chosen so that any isometric G-action on any metr ...
Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite permutation group ...
There is a growing need for unbiased clustering algorithms, ideally automated to analyze complex data sets. Topological data analysis (TDA) has been used to approach this problem. This recent field of mathematics discerns characteristic features of a space ...
The Tarski number of a nonamenable group is the smallest number of pieces needed for a paradoxical decomposition of the group. Nonamenable groups of piecewise projective homeomorphisms were introduced in [N. Monod, Groups of piecewise projective homeomorph ...
Using the Riemann Hypothesis over finite fields and bounds for the size of spherical codes, we give explicit upper bounds, of polynomial size with respect to the size of the field, for the number of geometric isomorphism classes of geometrically irreducibl ...
It is a well-known open problem since the 1970s whether a finitely generated perfect group can be normally generated by a single element or not. We prove that the topological version of this problem has an affirmative answer as long as we exclude infinite ...
The intersection graph of a collection C of sets is the graph on the vertex set C, in which C-1 . C-2 is an element of C are joined by an edge if and only if C-1 boolean AND C-2 not equal empty set. Erdos conjectured that the chromatic number of triangle-f ...
This paper presents a pseudo Wigner–Ville-distribution-based method in fringe projection for analyzing temporal behavior of the displacement derivative for a continuously deformed object. In the proposed method, a computer generated fringe pattern is proje ...
The E-star algorithm is a path planning method capable of dynamic replanning and user-configurable path cost interpolation. It calculates a navigation function as a sampling of an underlying smooth goal distance that takes into account a continuous notion ...
