Higher Dimensional Thompson Groups

We construct a "higher dimensional" version 2V of Thompson's group V. Like V it is an infinite, finitely presented, simple subgroup of the homeomorphism group of the Cantor set, but we show that it is not isomorphic to V by showing that the actions on the Cantor set are not topologically conjugate: 2V has an element with "chaotic" action, while V cannot have such an element. A theorem of Rubin is then applied which shows that for these two groups, isomorphism would imply topological conjugacy.Comment: 27 pages To appear in Geometriae Dedicat

The Free Group of Rank 2 is a Limit of Thompson's Group F

We show that the free group of rank 2 is a limit of 2-markings of Thompson's group F in the space of all 2-marked groups. More specifically, we find a sequence of generating pairs for F so that as one goes out the sequence, the length of the shortest relation satisfied by the generating pair goes to infinity.Comment: 19 pages, 19 figure

High energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows

We relate high-energy limits of Laplace-type and Dirac-type operators to frame flows on the corresponding manifolds, and show that the ergodicity of frame flows implies quantum ergodicity in an appropriate sense for those operators. Observables for the corresponding quantum systems are matrix-valued pseudodifferential operators and therefore the system remains non-commutative in the high-energy limit. We discuss to what extent the space of stationary high-energy states behaves classically.Comment: 26 pages, latex2

Automorphisms of generalized Thompson groups

We look at the automorphisms of Thompson type groups of piecewise linear homeomorphisms of the real line or circle that use slopes that are integral powers of a fixed integer n with n>2. We show that large numbers of "exotic" automorphisms appear---automorphisms that are represented as conjugation by non-PL homeomorphisms of the real line or circle. This is in contrast to the n=2 case where no such automorphisms appear.Comment: DVI and Post-Script files onl

The integration between corporate social responsibilty and sustainable development goals

Corporate Social Responsibility (CSR) is one of the modern concepts in the management field which become a catalyst in developing the future of the business sector. Several major academic and practical milestones have influenced the development of the concept of CSR. One of the most important milestones that shaped the future of CSR was the United Nations Global Compact (UNGC). UNGC's missions and principles formed an application framework for integrating social and environmental approaches into corporate business activities. It has been proved through this paper the interrelationship between the principles of CSR theories and the principles of UNGC. Followed by an analysis of the effectiveness of the UNGC principles in adopting sustainable development goals and enhancing enterprise competitiveness

Skinning measures in negative curvature and equidistribution of equidistant submanifolds

Let C be a locally convex subset of a negatively curved Riemannian manifold M. We define the skinning measure on the outer unit normal bundle to C in M by pulling back the Patterson-Sullivan measures at infinity, and give a finiteness result of skinning measures, generalising the work of Oh and Shah, with different methods. We prove that the skinning measures, when finite, of the equidistant hypersurfaces to C equidistribute to the Bowen-Margulis measure on the unit tangent bundle of M, assuming only that the Bowen-Margulis measure is finite and mixing for the geodesic flow. Under additional assumptions on the rate of mixing, we give a control on the rate of equidistribution.Comment: 32 pages. Revised version with important modifications to Section

Commentary on Robert Riley's article "A personal account of the discovery of hyperbolic structures on some knot complements"

We give some background and biographical commentary on the postumous article that appears in this [journal issue | ArXiv] by Robert Riley on his part of the early history of hyperbolic structures on some compact 3-manifolds. A complete list of Riley's publications appears at the end of the article.Comment: 5 page