1,822 research outputs found
The absence of efficient dual pairs of spanning trees in planar graphs
A spanning tree T in a finite planar connected graph G determines a dual
spanning tree T* in the dual graph G such that T and T* do not intersect. We
show that it is not always possible to find T in G, such that the diameters of
T and T* are both within a uniform multiplicative constant (independent of G)
of the diameters of their ambient graphs.Comment: 7 pages, 3 figure
Homologous non-isotopic symplectic tori in a K3-surface
For each member of an infinite family of homology classes in the K3-surface
E(2), we construct infinitely many non-isotopic symplectic tori representing
this homology class. This family has an infinite subset of primitive classes.
We also explain how these tori can be non-isotopically embedded as homologous
symplectic submanifolds in many other symplectic 4-manifolds including the
elliptic surfaces E(n) for n>2.Comment: 15 pages, 9 figures; v2: extended the main theorem, gave a second
construction of symplectic tori, added a figure, added/updated references,
minor changes in figure
Reconstructing the global topology of the universe from the cosmic microwave background
If the universe is multiply-connected and sufficiently small, then the last
scattering surface wraps around the universe and intersects itself. Each circle
of intersection appears as two distinct circles on the microwave sky. The
present article shows how to use the matched circles to explicitly reconstruct
the global topology of space.Comment: 6 pages, 2 figures, IOP format. To be published in the proceedings of
the Cleveland Cosmology and Topology Workshop 17-19 Oct 1997. Submitted to
Class. Quant. Gra
The Generalized Ricci Flow for 3D Manifolds with One Killing Vector
We consider 3D flow equations inspired by the renormalization group (RG)
equations of string theory with a three dimensional target space. By modifying
the flow equations to include a U(1) gauge field, and adding carefully chosen
De Turck terms, we are able to extend recent 2D results of Bakas to the case of
a 3D Riemannian metric with one Killing vector. In particular, we show that the
RG flow with De Turck terms can be reduced to two equations: the continual Toda
flow solved by Bakas, plus its linearizaton. We find exact solutions which flow
to homogeneous but not always isotropic geometries
Circles in the Sky: Finding Topology with the Microwave Background Radiation
If the universe is finite and smaller than the distance to the surface of
last scatter, then the signature of the topology of the universe is writ large
on the microwave background sky. We show that the microwave background will be
identified at the intersections of the surface of last scattering as seen by
different ``copies'' of the observer. Since the surface of last scattering is a
two-sphere, these intersections will be circles, regardless of the background
geometry or topology. We therefore propose a statistic that is sensitive to all
small, locally homogeneous topologies. Here, small means that the distance to
the surface of last scatter is smaller than the ``topology scale'' of the
universe.Comment: 14 pages, 10 figures, IOP format. This paper is a direct descendant
of gr-qc/9602039. To appear in a special proceedings issue of Class. Quant.
Grav. covering the Cleveland Topology & Cosmology Worksho
Cooperative program for design, fabrication, and testing of graphite/epoxy composite helicopter shafting
The fabrication of UH-1 helicopter tail rotor drive shafts from graphite/epoxy composite materials is discussed. Procedures for eliminating wrinkles caused by lack of precure compaction are described. The development of the adhesive bond between aluminum end couplings and the composite tube is analyzed. Performance tests to validate the superiority of the composite materials are reported
Measuring Topological Chaos
The orbits of fluid particles in two dimensions effectively act as
topological obstacles to material lines. A spacetime plot of the orbits of such
particles can be regarded as a braid whose properties reflect the underlying
dynamics. For a chaotic flow, the braid generated by the motion of three or
more fluid particles is computed. A ``braiding exponent'' is then defined to
characterize the complexity of the braid. This exponent is proportional to the
usual Lyapunov exponent of the flow, associated with separation of nearby
trajectories. Measuring chaos in this manner has several advantages, especially
from the experimental viewpoint, since neither nearby trajectories nor
derivatives of the velocity field are needed.Comment: 4 pages, 6 figures. RevTeX 4 with PSFrag macro
Right-veering diffeomorphisms of compact surfaces with boundary II
We continue our study of the monoid of right-veering diffeomorphisms on a
compact oriented surface with nonempty boundary, introduced in [HKM2]. We
conduct a detailed study of the case when the surface is a punctured torus; in
particular, we exhibit the difference between the monoid of right-veering
diffeomorphisms and the monoid of products of positive Dehn twists, with the
help of the Rademacher function. We then generalize to the braid group B_n on n
strands by relating the signature and the Maslov index. Finally, we discuss the
symplectic fillability in the pseudo-Anosov case by comparing with the work of
Roberts [Ro1,Ro2].Comment: 25 pages, 5 figure
Twin paradox and space topology
If space is compact, then a traveller twin can leave Earth, travel back home
without changing direction and find her sedentary twin older than herself. We
show that the asymmetry between their spacetime trajectories lies in a
topological invariant of their spatial geodesics, namely the homotopy class.
This illustrates how the spacetime symmetry invariance group, although valid
{\it locally}, is broken down {\it globally} as soon as some points of space
are identified. As a consequence, any non--trivial space topology defines
preferred inertial frames along which the proper time is longer than along any
other one.Comment: 6 pages, latex, 3 figure
Geometry and observables in (2+1)-gravity
We review the geometrical properties of vacuum spacetimes in (2+1)-gravity
with vanishing cosmological constant. We explain how these spacetimes are
characterised as quotients of their universal cover by holonomies. We explain
how this description can be used to clarify the geometrical interpretation of
the fundamental physical variables of the theory, holonomies and Wilson loops.
In particular, we discuss the role of Wilson loop observables as the generators
of the two fundamental transformations that change the geometry of
(2+1)-spacetimes, grafting and earthquake. We explain how these variables can
be determined from realistic measurements by an observer in the spacetime.Comment: Talk given at 2nd School and Workshop on Quantum Gravity and Quantum
Geometry (Corfu, September 13-20 2009); 10 pages, 13 eps figure
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