1,980 research outputs found
Spherical structures on torus knots and links
The present paper considers two infinite families of cone-manifolds endowed
with spherical metric. The singular strata is either the torus knot or the torus link . Domains of existence for a
spherical metric are found in terms of cone angles and volume formul{\ae} are
presented.Comment: 17 pages, 5 figures; typo
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
Analyticity of the Susceptibility Function for Unimodal Markovian Maps of the Interval
In a previous note [Ru] the susceptibility function was analyzed for some
examples of maps of the interval. The purpose of the present note is to give a
concise treatment of the general unimodal Markovian case (assuming real
analytic). We hope that it will similarly be possible to analyze maps
satisfying the Collet-Eckmann condition. Eventually, as explained in [Ru],
application of a theorem of Whitney [Wh] should prove differentiability of the
map restricted to a suitable set.Comment: 8 page
Quantum creation of an Inhomogeneous universe
In this paper we study a class of inhomogeneous cosmological models which is
a modified version of what is usually called the Lema\^itre-Tolman model. We
assume that we have a space with 2-dimensional locally homogeneous spacelike
surfaces. In addition we assume they are compact. Classically we investigate
both homogeneous and inhomogeneous spacetimes which this model describe. For
instance one is a quotient of the AdS space which resembles the BTZ black
hole in AdS.
Due to the complexity of the model we indicate a simpler model which can be
quantized easily. This model still has the feature that it is in general
inhomogeneous. How this model could describe a spontaneous creation of a
universe through a tunneling event is emphasized.Comment: 21 pages, 5 ps figures, REVTeX, new subsection include
Comments on Closed Bianchi Models
We show several kinematical properties that are intrinsic to the Bianchi
models with compact spatial sections. Especially, with spacelike hypersurfaces
being closed, (A) no anisotropic expansion is allowed for Bianchi type V and
VII(A\not=0), and (B) type IV and VI(A\not=0,1) does not exist. In order to
show them, we put into geometric terms what is meant by spatial homogeneity and
employ a mathematical result on 3-manifolds. We make clear the relation between
the Bianchi type symmetry of space-time and spatial compactness, some part of
which seem to be unnoticed in the literature. Especially, it is shown under
what conditions class B Bianchi models do not possess compact spatial sections.
Finally we briefly describe how this study is useful in investigating global
dynamics in (3+1)-dimensional gravity.Comment: 14 pages with one table, KUCP-5
Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
We construct an exactly solvable Hamiltonian acting on a 3-dimensional
lattice of spin- systems that exhibits topological quantum order.
The ground state is a string-net and a membrane-net condensate. Excitations
appear in the form of quasiparticles and fluxes, as the boundaries of strings
and membranes, respectively. The degeneracy of the ground state depends upon
the homology of the 3-manifold. We generalize the system to , were
different topological phases may occur. The whole construction is based on
certain special complexes that we call colexes.Comment: Revtex4 file, color figures, minor correction
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
S^1 \times S^2 as a bag membrane and its Einstein-Weyl geometry
In the hybrid skyrmion in which an Anti-de Sitter bag is imbedded into the
skyrmion configuration a S^{1}\times S^{2} membrane is lying on the
compactified spatial infinity of the bag [H. Rosu, Nuovo Cimento B 108, 313
(1993)]. The connection between the quark degrees of freedom and the mesonic
ones is made through the membrane, in a way that should still be clarified from
the standpoint of general relativity and topology. The S^1 \times S^2 membrane
as a 3-dimensional manifold is at the same time a Weyl-Einstein space. We make
here an excursion through the mathematical body of knowledge in the
differential geometry and topology of these spaces which is expected to be
useful for hadronic membranesComment: 9pp in latex, minor correction
Locally U(1)*U(1) Symmetric Cosmological Models: Topology and Dynamics
We show examples which reveal influences of spatial topologies to dynamics,
using a class of spatially {\it closed} inhomogeneous cosmological models. The
models, called the {\it locally U(1)U(1) symmetric models} (or the {\it
generalized Gowdy models}), are characterized by the existence of two commuting
spatial {\it local} Killing vectors. For systematic investigations we first
present a classification of possible spatial topologies in this class. We
stress the significance of the locally homogeneous limits (i.e., the Bianchi
types or the `geometric structures') of the models. In particular, we show a
method of reduction to the natural reduced manifold, and analyze the
equivalences at the reduced level of the models as dynamical models. Based on
these fundamentals, we examine the influence of spatial topologies on dynamics
by obtaining translation and reflection operators which commute with the
dynamical flow in the phase space.Comment: 32 pages, 1 figure, LaTeX2e, revised Introduction slightly. To appear
in CQ
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