8,162 research outputs found
On the distortion of knots on embedded surfaces
Our main result is a nontrivial lower bound for the distortion of some
specific knots. In particular, we show that the distortion of the torus knot
satisfies . This answers a
1983 question of Gromov
Limiting Case of Modified Electroweak Model for Contracted Gauge Group
The modification of the Electroweak Model with 3-dimensional spherical
geometry in the matter fields space is suggested. The Lagrangian of this model
is given by the sum of the {\it free} (without any potential term) matter
fields Lagrangian and the standard gauge fields Lagrangian. The vector boson
masses are generated by transformation of this Lagrangian from Cartesian
coordinates to a coordinates on the sphere . The limiting case of the
bosonic part of the modified model, which corresponds to the contracted gauge
group is discussed. Within framework of the limit model
Z-boson and electromagnetic fields can be regarded as an external ones with
respect to W-bosons fields in the sence that W-boson fields do not effect on
these external fields. The masses of all particles of the Electroweak Model
remain the same, but field interactions in contracted model are more simple as
compared with the standard Electroweak Model.Comment: 12 pages, talk given at the XIII Int. Conf. on SYMMETRY METHODS IN
PHYSICS, Dubna, Russia, July 6-9, 2009; added references for introduction,
clarified motivatio
A Lower Bound on the Waist of Unit Spheres of Uniformly Convex Normed Spaces
In this paper we give a lower bound on the waist of the unit sphere of a
uniformly convex normed space by using the localization technique in
codimension greater than one and a strong version of the Borsuk-Ulam theorem.
The tools used in this paper follow ideas of M. Gromov in [4]. Our
isoperimetric type inequality generalizes the Gromov-Milman isoperimetric
inequality in [5].Comment: 36 page
Generalized Scaling Function at Strong Coupling
We considered folded spinning string in AdS_5 x S^5 background dual to the
Tr(D^S Phi^J) operators of N=4 SYM theory. In the limit S,J-> \infty and l=pi
J/\sqrt\lambda\log S fixed we compute the string energy with the 2-loop
accuracy in the worldsheet coupling \sqrt\lambda from the asymptotical Bethe
ansatz. In the limit l-> 0 the result is finite due to the massive cancelations
with terms coming from the conjectured dressing phase. We also managed to
compute all leading logarithm terms l^{2m}\log^n l/\lambda^n/2 to an arbitrary
order in perturbation theory. In particular for m=1 we reproduced results of
Alday and Maldacena computed from a sigma model. The method developed in this
paper could be used for a systematic expansion in 1/\sqrt\lambda and also at
weak coupling
A flat plane that is not the limit of periodic flat planes
We construct a compact nonpositively curved squared 2-complex whose universal
cover contains a flat plane that is not the limit of periodic flat planes.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-6.abs.htm
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