Braid lift representations of Artin's Braid Group

2000 ◽  
Vol 09 (08) ◽  
pp. 1005-1009
Author(s):  
Reinhard Häring-Oldenburg
Keyword(s):  
Braid Group ◽  
Braid Groups ◽  
Finite Dimensional ◽  
Braid Theory

We recast the braid-lift representation of Contantinescu, Lüdde and Toppan in the language of B-type braid theory. Composing with finite dimensional representations of these braid groups we obtain various sequences of finite dimensional multi-parameter representations.

Braid Description of Few Body Dynamics

1998 ◽  
Vol 08 (07) ◽  
pp. 1383-1397 ◽  
Author(s):  
Sigmund Clausen ◽  
Geir Helgensen ◽  
Arne T. Skjeltorp
Keyword(s):  
Magnetic Fields ◽  
Periodic Orbits ◽  
Phase Portraits ◽  
Body System ◽  
Body Dynamics ◽  
Braid Theory ◽  
Phase Phase

A few body system of magnetic holes set in motion by external ac magnetic fields is studied both experimentally and numerically. Notions from braid theory are used to describe the dynamics ina very compact manner. The time histroy of n magnetic holes moving in a plane is represented by an n-strand braid which enables us to extrat periodic orbits and to map out phase phase portraits. The transitions between different periodic modes of motion are either continuous or noncontinuous followed by strong hysteresis.

Rotations of 4nπ Research and no Twisted Mechanism Example Analysis Based on the Theory of Braid Group

2014 ◽  
Vol 536-537 ◽  
pp. 1355-1360
Author(s):  
Zhi Yu Fu ◽  
Lu Bin Hang ◽  
Hai Xu ◽  
Jin Cai ◽  
Huai Qiang Bian ◽  
...  
Keyword(s):  
Group Theory ◽  
Mechanism Design ◽  
Braid Group ◽  
Twisted State ◽  
Braid Theory

The Cable or Pipe between the Two Relatively Rotating Platforms Exists the Twisted Problem. from Viewpoint of Braid Group Theory, Rope’s Twisted State is Researched on. Based on the Characteristics of a Special Garside Braids Δn and Δnk , the Equivalence of Two Rotation Modes is Revealed. also, that the Determination of Rotation Mode’s Minimum Rotate Range is 4∏ while Using Braid Theory is Proposed. the Theory of Braid Group can Not only be Used as a Criterion for Determine Whether the Cable is Twisted, Finally, but also can be Used as Avoid Cable Twisted during Mechanism Design.

scholarly journals Closed braids and knot holders associated to some laser dynamical systems: A pump-modulated Nd-doped Â…ber laser

2017 ◽  
Vol 12 (12) ◽  
pp. 6894-6900
Author(s):  
Elsaued Elrifai
Keyword(s):  
Dynamical Systems ◽  
Fiber Laser ◽  
Crossing Number ◽  
Topological Invariants ◽  
Control Parameters ◽  
Linking Number ◽  
Fibered Knots ◽  
Braid Theory ◽  
Knots And Links

In this work the arising knots and links for the pump-modulated Nd-doped fiber laser is investigated. For the associated templates, some of their topological invariants, such as braid linking matrix, braid words, crossing number and linking number, are studied. It is recognized that the derived topological invariants are quietly dependent on the control parameters Using the tools of the braid theory, it is shown that pump-modulated Nd-doped fiber laser knots and links are positive fibered knots and links.

Quantum genetic spiral the space-time

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Dominant Gene ◽  
Space Time ◽  
Mathematical Form ◽  
Time Axis ◽  
Quantum Darwinism ◽  
Braid Theory ◽  
Concept Of Information ◽  
Selection Of

The nature of quantum mechanics has various interpretations. In this paper we consider the hypothesis of quantum Darwinism. Quantum theory is closely connected with the concept of information. Perhaps there is an analogue of the genetic code for quantum Darwinism. Here the attempt of the genetic formulation of quantum gravity. It is based on the idea of the quantum genetic spiral the space-time, directed along the time axis. Such a mathematical form exists in braid theory. Matter how information is coded in the genetic structure of space-time. Natural and artificial selection of quantum Darwinism leads to the collapse of the wave function and the identification of a dominant gene.

On marked braid groups

2015 ◽  
Vol 24 (13) ◽  
pp. 1541005 ◽  
Author(s):  
Denis A. Fedoseev ◽  
Vassily O. Manturov ◽  
Zhiyun Cheng
Keyword(s):  
Braid Group ◽  
Knot Theory ◽  
Braid Groups ◽  
Arbitrary Group ◽  
Natural Group ◽  
Additional Information ◽  
Reidemeister Moves ◽  
Braid Theory ◽  
Important Notion

In this paper, we introduce [Formula: see text]-braids and, more generally, [Formula: see text]-braids for an arbitrary group [Formula: see text]. They form a natural group-theoretic counterpart of [Formula: see text]-knots, see [V. O. Manturov; Reidemeister moves and groups, preprint (2014), arXiv:1412.8691]. The underlying idea used in the construction of these objects — decoration of crossings with some additional information — generalizes an important notion of parity introduced by the second author (see [V. O. Manturov, Parity in knot theory, Sb. Math. 201(5) (2010) 693–733]) to different combinatorically geometric theories, such as knot theory, braid theory and others. These objects act as natural enhancements of classical (Artin) braid groups. The notion of dotted braid group is introduced: classical (Artin) braid groups live inside dotted braid groups as those elements having presentation with no dots on the strands. The paper is concluded by a list of unsolved problems.

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