8,591 research outputs found
Heegaard diagrams and surgery descriptions for twisted face-pairing 3-manifolds
The twisted face-pairing construction of our earlier papers gives an
efficient way of generating, mechanically and with little effort, myriads of
relatively simple face-pairing descriptions of interesting closed 3-manifolds.
The corresponding description in terms of surgery, or Dehn-filling, reveals the
twist construction as a carefully organized surgery on a link.
In this paper, we work out the relationship between the twisted face-pairing
description of closed 3-manifolds and the more common descriptions by surgery
and Heegaard diagrams. We show that all Heegaard diagrams have a natural
decomposition into subdiagrams called Heegaard cylinders, each of which has a
natural shape given by the ratio of two positive integers. We characterize the
Heegaard diagrams arising naturally from a twisted face-pairing description as
those whose Heegaard cylinders all have integral shape. This characterization
allows us to use the Kirby calculus and standard tools of Heegaard theory to
attack the problem of finding which closed, orientable 3-manifolds have a
twisted face-pairing description.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-10.abs.htm
The Algebra of Strand Splitting. II. A Presentation for the Braid Group on One Strand
Presentations are computed for a braided version BV of Thompson's group V and
for V itself showing that there is an Artin group/Coxeter group relation
between them. The presentation for V is obtained from that for BV by declaring
all that all generators are involutions.Comment: 15 page
Universal shape ratios for polymers grafted at a flat surface
We consider dilute non-adsorbed polymers grafted at an impenetrable surface
and compute several quantities which characterize the polymer shape: the
asphericity and the ratios of the eigenvalues of the radius-of-gyration tensor.
The results are only slightly different from those obtained for polymers in the
bulk, showing that the surface has little influence on the polymer shape.Comment: 10 pages, LaTe
Point vortices on the hyperbolic plane
We investigate some properties of the dynamical system of point vortices on
the hyperboloid. This system has noncompact symmetry SL(2, R) and a coadjoint
equivariant momentum map J. The relative equilibrium conditions are found and
the trajectories of relative equilibria with non-zero momentum value are
described. We also provide the classification of relative equilibria and the
stability criteria for a number of cases, focusing on N=2, 3. Contrary to the
system on the sphere, relative equilibria with non-compact momentum isotropy
subgroup are found, and are used to illustrate the different stability types of
relative equilibria.Comment: To appear in J. Mathematical Physic
The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V
We construct a braided version of Thompson's group V.Comment: 27 page
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