4,347 research outputs found
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
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