650 research outputs found
Eliashberg's proof of Cerf's theorem
Following a line of reasoning suggested by Eliashberg, we prove Cerf's
theorem that any diffeomorphism of the 3-sphere extends over the 4-ball. To
this end we develop a moduli-theoretic version of Eliashberg's
filling-with-holomorphic-discs method.Comment: 32 page
Procedure for measurement of logarithmic growth
Measurement of logarithmic growt
Casimir effect with a helix torus boundary condition
We use the generalized Chowla-Selberg formula to consider the Casimir effect
of a scalar field with a helix torus boundary condition in the flat
()-dimensional spacetime.
We obtain the exact results of the Casimir energy density and pressure for
any for both massless and massive scalar fields. The numerical calculation
indicates that once the topology of spacetime is fixed, the ratio of the sizes
of the helix will be a decisive factor. There is a critical value of
the ratio of the lengths at which the pressure vanishes. The pressure
changes from negative to positive as the ratio passes through
increasingly. In the massive case, we find the pressure tends to the result of
massless field when the mass approaches zero. Furthermore, there is another
critical ratio of the lengths and the pressure is
independent of the mass at in the D=3 case.Comment: 11 pages, 3 figures, to be published in Mod. Phys. Lett.
Schrijver graphs and projective quadrangulations
In a recent paper [J. Combin. Theory Ser. B}, 113 (2015), pp. 1-17], the
authors have extended the concept of quadrangulation of a surface to higher
dimension, and showed that every quadrangulation of the -dimensional
projective space is at least -chromatic, unless it is bipartite.
They conjectured that for any integers and , the
Schrijver graph contains a spanning subgraph which is a
quadrangulation of . The purpose of this paper is to prove the
conjecture
Betti number signatures of homogeneous Poisson point processes
The Betti numbers are fundamental topological quantities that describe the
k-dimensional connectivity of an object: B_0 is the number of connected
components and B_k effectively counts the number of k-dimensional holes.
Although they are appealing natural descriptors of shape, the higher-order
Betti numbers are more difficult to compute than other measures and so have not
previously been studied per se in the context of stochastic geometry or
statistical physics.
As a mathematically tractable model, we consider the expected Betti numbers
per unit volume of Poisson-centred spheres with radius alpha. We present
results from simulations and derive analytic expressions for the low intensity,
small radius limits of Betti numbers in one, two, and three dimensions. The
algorithms and analysis depend on alpha-shapes, a construction from
computational geometry that deserves to be more widely known in the physics
community.Comment: Submitted to PRE. 11 pages, 10 figure
Skew Category Algebras Associated with Partially Defined Dynamical Systems
We introduce partially defined dynamical systems defined on a topological
space. To each such system we associate a functor from a category to
\Top^{\op} and show that it defines what we call a skew category algebra . We study the connection between topological freeness of
and, on the one hand, ideal properties of and, on
the other hand, maximal commutativity of in . In
particular, we show that if is a groupoid and for each e \in \ob(G) the
group of all morphisms is countable and the topological space
is Tychonoff and Baire, then the following assertions are equivalent:
(i) is topologically free; (ii) has the ideal intersection property,
that is if is a nonzero ideal of , then ; (iii) the ring is a maximal abelian complex subalgebra of . Thereby, we generalize a result by Svensson, Silvestrov
and de Jeu from the additive group of integers to a large class of groupoids.Comment: 16 pages. This article is an improvement of, and hereby a replacement
for, version 1 (arXiv:1006.4776v1) entitled "Category Dynamical Systems and
Skew Category Algebras
Topology of the three-qubit space of entanglement types
The three-qubit space of entanglement types is the orbit space of the local
unitary action on the space of three-qubit pure states, and hence describes the
types of entanglement that a system of three qubits can achieve. We show that
this orbit space is homeomorphic to a certain subspace of R^6, which we
describe completely. We give a topologically based classification of
three-qubit entanglement types, and we argue that the nontrivial topology of
the three-qubit space of entanglement types forbids the existence of standard
states with the convenient properties of two-qubit standard states.Comment: 9 pages, 3 figures, v2 adds a referenc
A Local Computation Approximation Scheme to Maximum Matching
We present a polylogarithmic local computation matching algorithm which
guarantees a (1-\eps)-approximation to the maximum matching in graphs of
bounded degree.Comment: Appears in Approx 201
Isolation of subcellular fractions of Nuerospora of mycelio
Isolation of subcellular fraction
Inverse monoids and immersions of 2-complexes
It is well known that under mild conditions on a connected topological space
, connected covers of may be classified via conjugacy
classes of subgroups of the fundamental group of . In this paper,
we extend these results to the study of immersions into 2-dimensional
CW-complexes. An immersion between
CW-complexes is a cellular map such that each point has a
neighborhood that is mapped homeomorphically onto by . In order
to classify immersions into a 2-dimensional CW-complex , we need to
replace the fundamental group of by an appropriate inverse monoid.
We show how conjugacy classes of the closed inverse submonoids of this inverse
monoid may be used to classify connected immersions into the complex
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