390 research outputs found
Topological regluing of rational functions
Regluing is a topological operation that helps to construct topological
models for rational functions on the boundaries of certain hyperbolic
components. It also has a holomorphic interpretation, with the flavor of
infinite dimensional Thurston--Teichm\"uller theory. We will discuss a
topological theory of regluing, and trace a direction in which a holomorphic
theory can develop.Comment: 38 page
Space-time directional Lyapunov exponents for cellular automata
Space-time directional Lyapunov exponents are introduced. They describe the
maximal velocity of propagation to the right or to the left of fronts of
perturbations in a frame moving with a given velocity. The continuity of these
exponents as function of the velocity and an inequality relating them to the
directional entropy is proved
Multi-Bunch Solutions of Differential-Difference Equation for Traffic Flow
Newell-Whitham type car-following model with hyperbolic tangent optimal
velocity function in a one-lane circuit has a finite set of the exact solutions
for steady traveling wave, which expressed by elliptic theta function. Each
solution of the set describes a density wave with definite number of
car-bunches in the circuit. By the numerical simulation, we observe a
transition process from a uniform flow to the one-bunch analytic solution,
which seems to be an attractor of the system. In the process, the system shows
a series of cascade transitions visiting the configurations closely similar to
the higher multi-bunch solutions in the set.Comment: revtex, 7 pages, 5 figure
Homotopy on spatial graphs and generalized Sato-Levine invariants
Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs
which are generalizations of Milnor's link-homotopy. Fleming and the author
introduced some edge (resp. vertex)-homotopy invariants of spatial graphs by
applying the Sato-Levine invariant for the constituent 2-component
algebraically split links. In this paper, we construct some new edge (resp.
vertex)-homotopy invariants of spatial graphs without any restriction of
linking numbers of the constituent 2-component links by applying the
generalized Sato-Levine invariant.Comment: 16 pages, 13 figure
Discrete Morse functions for graph configuration spaces
We present an alternative application of discrete Morse theory for
two-particle graph configuration spaces. In contrast to previous constructions,
which are based on discrete Morse vector fields, our approach is through Morse
functions, which have a nice physical interpretation as two-body potentials
constructed from one-body potentials. We also give a brief introduction to
discrete Morse theory. Our motivation comes from the problem of quantum
statistics for particles on networks, for which generalized versions of anyon
statistics can appear.Comment: 26 page
Combinatorial expression for universal Vassiliev link invariant
The most general R-matrix type state sum model for link invariants is
constructed. It contains in itself all R-matrix invariants and is a generating
function for "universal" Vassiliev link invariants. This expression is more
simple than Kontsevich's expression for the same quantity, because it is
defined combinatorially and does not contain any integrals, except for an
expression for "the universal Drinfeld's associator".Comment: 20 page
Stein structures: existence and flexibility
This survey on the topology of Stein manifolds is an extract from our recent
joint book. It is compiled from two short lecture series given by the first
author in 2012 at the Institute for Advanced Study, Princeton, and the Alfred
Renyi Institute of Mathematics, Budapest.Comment: 29 pages, 11 figure
Two-Dimensional Dilaton-Gravity Coupled to Massless Spinors
We apply a global and geometrically well-defined formalism for
spinor-dilaton-gravity to two-dimensional manifolds. We discuss the general
formalism and focus attention on some particular choices of the dilatonic
potential. For constant dilatonic potential the model turns out to be
completely solvable and the general solution is found. For linear and
exponential dilatonic potentials we present the class of exact solutions with a
Killing vector.Comment: 21 pages, LaTeX, minor changes in text and format, final version to
appear in Classical and Quantum Gravit
Cohomology of bundles on homological Hopf manifold
We discuss the properties of complex manifolds having rational homology of
including those constructed by Hopf, Kodaira and
Brieskorn-van de Ven. We extend certain previously known vanishing properties
of cohomology of bundles on such manifolds.As an application we consider
degeneration of Hodge-deRham spectral sequence in this non Kahler setting.Comment: To appear in Proceedings of 2007 conference on Several complex
variables and Complex Geometry. Xiamen. Chin
Morse index and causal continuity. A criterion for topology change in quantum gravity
Studies in 1+1 dimensions suggest that causally discontinuous topology
changing spacetimes are suppressed in quantum gravity. Borde and Sorkin have
conjectured that causal discontinuities are associated precisely with index 1
or n-1 Morse points in topology changing spacetimes built from Morse functions.
We establish a weaker form of this conjecture. Namely, if a Morse function f on
a compact cobordism has critical points of index 1 or n-1, then all the Morse
geometries associated with f are causally discontinuous, while if f has no
critical points of index 1 or n-1, then there exist associated Morse geometries
which are causally continuous.Comment: Latex, 20 pages, 3 figure
- …