Orbifold construction of the modes of the Poincaré dodecahedral space

The Poincaré Dodecahedral Space and the Mystery of the Missing Fluctuations, Volume 51, Number 6

Harmonic Polynomials on the Poincaré Dodecahedral Three-manifold

The global topology of the three-space is not fixed by Einstein general relativity, since this is formulated in terms of local differential equations. Einstein’s first static cosmological models used for the space-part of the universe a simply connected sphere S3. With present-day cosmological information it becomes possible to propose and test multiply-connected topologies for the space-part o...

Knot complements, hidden symmetries and reflection orbifolds

In this article we examine the conjecture of Neumann and Reid that the only hyperbolic knots in the 3-sphere which admit hidden symmetries are the figure-eight knot and the two dodecahedral knots. Knots whose complements cover hyperbolic reflection orbifolds admit hidden symmetries, and we verify the Neumann-Reid conjecture for knots which cover small hyperbolic reflection orbifolds. We also sh...

Finiteness Properties for Some Rational Poincaré Duality Groups

A combination of Bestvina–Brady Morse theory and an acyclic reflection group trick produces a torsion-free finitely presented Q-Poincaré duality group which is not the fundamental group of an aspherical closed ANR Q-homology manifold. The acyclic construction suggests asking which Q-Poincaré duality groups act freely on Q-acyclic spaces (i.e., which groups are FH(Q)). For example, the orbifold ...

Near-Minimum Time Optimal Control of Flexible Spacecraft during Slewing Maneuver

The rapid growth of space utilization requires extensive construction, and maintenance of space structures and satellites in orbit. &#10This will, in turn, substantiate application of robotic systems in space. In this paper, a near-minimum-time optimal control law is developed for a rigid space platform with flexible links during an orientating maneuver with large angle of rotation. The time op...