70,096 research outputs found
Configurations, and parallelograms associated to centers of mass
The purpose of this article is to
\begin{enumerate}
\item define the -fold center of mass arrangement for points
in the plane,
\item give elementary properties of and
\item give consequences concerning the space of distinct points
in the plane, no four of which are the vertices of a parallelogram.
\end{enumerate}
The main result proven in this article is that the classical unordered
configuration of points in the plane is not a retract up to homotopy of the
space of unordered distinct points in the plane, no four of which are the
vertices of a parallelogram. The proof below is homotopy theoretic without an
explicit computation of the homology of these spaces.
In addition, a second, speculative part of this article arises from the
failure of these methods in the case of odd primes . This failure gives rise
to a candidate for the localization at odd primes of the double loop space
of an odd sphere obtained from the -fold center of mass arrangement.
Potential consequences are listed.Comment: 11 page
On injective homomorphisms for pure braid groups, and associated Lie algebras
The question of whether a representation of Artin's pure braid group is
faithful is translated to certain properties of the Lie algebra arising from
the descending central series of the pure braid group, and thus the Vassiliev
invariants of pure braids via work of T. Kohno \cite{kohno1,kohno2}. The main
result is a Lie algebraic condition which guarantees that a homomorphism out of
the classical pure braid group is faithful. However, it is unclear whether the
methods here can be applied to any open cases such as the Gassner
representation.Comment: Change in Contex
The stable braid group and the determinant of the Burau representation
This article gives certain fibre bundles associated to the braid groups which
are obtained from a translation as well as conjugation on the complex plane.
The local coefficient systems on the level of homology for these bundles are
given in terms of the determinant of the Burau representation.
De Concini, Procesi, and Salvetti [Topology 40 (2001) 739--751] considered
the cohomology of the n-th braid group B_n with local coefficients obtained
from the determinant of the Burau representation, H^*(B_n;Q[t^{+/-1}]). They
show that these cohomology groups are given in terms of cyclotomic fields.
This article gives the homology of the stable braid group with local
coefficients obtained from the determinant of the Burau representation. The
main result is an isomorphism
H_*(B_infty; F[t^{+/-1}])-->H_*(Omega^2S^3; F) for any field F where
Omega^2S^3 denotes the double loop space of the 3-connected cover of the
3-sphere. The methods are to translate the structure of H_*(B_n;F[t^{+/-1}]) to
one concerning the structure of the homology of certain function spaces where
the answer is computed.Comment: This is the version published by Geometry & Topology Monographs on 29
January 200
On the Andreadakis-Johnson filtration of the automorphism group of a free group
The Johnson filtration of the automorphism group of a free group is composed
of those automorphisms which act trivially on nilpotent quotients of the free
group. We compute cohomology classes as follows: (i) we analyze analogous
classes for a subgroup of the pure symmetric automorphism group of a free
group, and (ii) we analyze features of these classes which are preserved by the
Johnson homomorphism. One consequence is that the ranks of the cohomology
groups in any fixed dimension between 1 and n-1 increase without bound for
terms deep in the Johnson filtraton.Comment: Corrections; revisions to proof of main theore
pi N --> Multi-pi N Scattering in the 1/N_c Expansion
We extend the 1/N_c expansion meson-baryon scattering formalism to cases in
which the final state contains more than two particles. We first show that the
leading-order large N_c processes proceed through resonant intermediate states
(e.g., rho N or pi Delta). We then tabulate linear amplitude expressions for
relevant processes and find that the pole structure of baryon resonances can be
uniquely identified by their (non)appearance in eta N or mixed partial-wave pi
Delta final states. We also show that quantitative predictions of pi N to pi
Delta branching ratios predicted at leading order alone do not agree with
measurements, but the inclusion of 1/N_c corrections is ample to explain the
discrepancies.Comment: 23 pages, 3 eps figures, ReVTeX4, added reference and discussion,
identical to PRD versio
Standardized Pearson type 3 density function area tables
Tables constituting extension of similar tables published in 1936 are presented in report form. Single and triple parameter gamma functions are discussed. Report tables should interest persons concerned with development and use of numerical analysis and evaluation methods
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