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Generalized Braid group on the Sphere
the spherical braid group or Hurwitz braid group is a braid group on n strands. In comparison with the usual braid group, it has an additional group relation
Spherical_braid_group
Group whose operation is a composition of braids
In mathematics, the braid group on n strands (denoted B n {\displaystyle B_{n}} ), also known as the Artin braid group, is the group whose elements are
Braid_group
Family of infinite discrete groups
mathematical area of group theory, Artin groups, also known as Artin–Tits groups or generalized braid groups, are a family of infinite discrete groups defined by
Artin–Tits_group
Mathematical group
generalized braid group is said to be of spherical type if the associated Coxeter group is finite. If B is a generalized braid group of spherical type, then
Parabolic subgroup of a reflection group
Parabolic_subgroup_of_a_reflection_group
Alexander polynomial Jones polynomial Knot group Writhe Quandle Seifert surface Braids Braid theory Braid group Kirby calculus Genus (mathematics) Examples
List of geometric topology topics
List_of_geometric_topology_topics
Deformation of the group algebra of a Coxeter group
algebra of a Coxeter group. Hecke algebras are quotients of the group rings of Artin braid groups. This connection found a spectacular application in Vaughan
Iwahori–Hecke_algebra
Type of monoidal category
a braided spherical fusion category with non-degenerate braiding. In the presence of a braiding, Deligne's twisting lemma states that a spherical structure
Modular_tensor_category
Method of representing a 3D object by defining the limits of its volume
the early 1970s by both Ian C. Braid in Cambridge (for CAD) and Bruce G. Baumgart at Stanford (for computer vision). Braid continued his work with the research
Boundary_representation
Branch of topology
topics are the theory of 3-manifolds and 4-manifolds, knot theory, and braid groups. This can be regarded as a part of geometric topology. It may also be
Low-dimensional_topology
Rowell, Eric C. (2021). "Rank-finiteness for G-crossed braided fusion categories". Transformation Groups. 26: 915–927. arXiv:1902.06165. doi:10.1007/s00031-020-09576-2
Rank-finiteness
Loop seen as a trivial knot
however, only one new crossing needs to be introduced when working with spherical Reidemeister moves.) Many other examples exist such as "the Monster" created
Unknot
(quantum mechanics) particle in a box particle in a ring particle in a spherically symmetric potential quantum harmonic oscillator hydrogen atom ring wave
List of mathematical topics in quantum theory
List_of_mathematical_topics_in_quantum_theory
Human hair texture
hair braiding was not a paid trade.[citation needed] When men from the Wolof tribe (in modern Senegal and The Gambia) went to war they wore a braided style
Kinky_hair
Ranged weapon to throw projectiles
it is made of bast fibre (almost certainly flax) twine; the cords are braided in a 10-strand elliptical sennit and the cradle seems to have been woven
Sling_(weapon)
category" and "unitary spherical fusion category". Thus, a unitary modular tensor category can be defined as a unitary braided fusion category, with no
Unitary modular tensor category
Unitary_modular_tensor_category
paths and loops lead to knot theory, and related structures such as links, braids, and tangles. Riemannian manifolds are special cases of metric spaces, and
Maps_of_manifolds
Branch of differential geometry and differential topology
Previously, the "symplectic group" had been called the "line complex group". "Complex" comes from the Latin com-plexus, meaning "braided together" (co- + plexus)
Symplectic_geometry
Uniforms of the army of Napoleon I
of pewter buttons and thirteen to eighteen rows of braid, and was richly trimmed with white braid along the seams, the collar, and the lapels. Officers
Uniforms_of_the_Grande_Armée
Ethnic group in Japan and Russia
Tourist Industry, Japanese Government Railways. p. 30. One is a nettle-hemp braid named pon kut (small sash) or ra-nn kut (under sash). "Ainu | Definition
Ainu_people
List of particles in matter including fermions and bosons
and bosons in two-dimensional systems like sheets of graphene that obeys braid statistics. Excitons are bound states of an electron and a hole. Magnons
List_of_particles
exchange protocol, whose security is based on assumptions about the braid group. This series culminates in Miasnikov and Ushakov (2008) which applies
Generic-case_complexity
Fictional protagonist of Tomb Raider
baseball cap". He settled on a tough South American Latina woman with a braid named Laura Cruz. Tomb Raider co-creator Paul Douglas changed her given
Lara_Croft
Spanish mathematician (born 1992)
geometric group theory and has succeeded in generalizing geometric and topological results on braid groups to the algebraic context of Artin-Tits groups of spherical
María_Cumplido
ISBN 1-57955-008-8. Douglas Hofstadter (1979). Gödel, Escher, Bach: an Eternal Golden Braid. New York: Basic Books. ISBN 0-465-02656-7. Here: Introduction / Consistency
History_of_mathematics
American home appliance company
suction hose in the industry. Other cleaners at the time were using cloth-braided hoses, which would deteriorate and lose suction over time. In 1954, Herbert
The_Hoover_Company
Chemical element with atomic number 79 (Au)
where archean rivers from the north and north-west formed extensive pebbly Braided river deltas before draining into the "Witwatersrand sea" where the rest
Gold
Chinese characters used in modern languages
heart), 座 (zuò, seat), 旗 (qí, flag); Inner meaning and outer sound: 辮 (biàn, braid), 悶 (mèn, dull), 摹 (mó, imitation). Semantic-form characters are composed
Modern_Chinese_characters
History of maths
categories. The most common examples include: ribbon categories, braided tensor categories, spherical categories, compact closed categories, symmetric tensor categories
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
Archived from the original on September 26, 2008. Kimmerer, Robin Wall. Braiding Sweetgrass. Milkweed Editions. pp. 109–111. Cope, Nigel (August 7, 1997)
List_of_candies
1991 film directed by Nicholas Meyer
Klingon took three and a half hours. Hairstylist Jan Alexander designed braids and jewelry that suggested a tribal people with a long and treasured heritage
Star Trek VI: The Undiscovered Country
Star_Trek_VI:_The_Undiscovered_Country
of fines content ISO 1436:2020 Rubber hoses and hose assemblies — Wire-braid-reinforced hydraulic types for oil-based or water-based fluids — Specification
List_of_ISO_standards_1–1999
Ancient Roman town in Campania, Italy
from the Campi Flegrei Archaeological Park. The mosaic included crossing braids and hexagons with concave sides. Among the most significant and remarkable
Baiae
Traditional religion of Lakota people
During this period, the seeker will be largely naked and have their hair un-braided as a sign of humility to the spirits. This is to ensure that they are pitiable
Lakota_religion
rates of lactase persistence. However, some indigenous sociolinguistic groups in regions of the country, such as Inner Mongolia, Tibet and Yunnan, have
List_of_cheeses
Team sport played with a ball
review". Journal of Clinical Medicine. 10 (9): 2029. Sadigursky, David; Braid, Juliana Almeida; Lemos De Lira, Diogo Neiva; Machado, Bruno Almeida Barreto;
Association_football
Armenian traditional clothing
special wealth and beauty. The girls braided their hair in numerous braids (up to 40), of which the front braids were thrown forward on the chest and
Armenian_dress
Algebraic object with geometric applications
represent momentum fluxes Spherical tensor operators are the eigenfunctions of the quantum angular momentum operator in spherical coordinates Diffusion tensors
Tensor
existing astrolabes, Richard developed the rectangulus as an instrument for spherical trigonometry and to measure the angles between planets and other astronomical
List of British innovations and discoveries
List_of_British_innovations_and_discoveries
Dutch graphic artist (1898–1972)
Hofstadter, Douglas R. (1999) [1979]. Gödel, Escher, Bach: An Eternal Golden Braid. Basic Books. ISBN 978-0-465-02656-2. Schmadel, Lutz D. (2012). Dictionary
M._C._Escher
regions, and typically characterized by various fluvial landforms such as braided streams, terraces, and meanders. Alluvial plains encompass the larger area
Glossary of geography terms (A–M)
Glossary_of_geography_terms_(A–M)
Category admitting tensor products
mathematical foundation for the topological order in condensed matter physics. Braided monoidal categories have applications in quantum information, quantum field
Monoidal_category
Ethnolinguistic group in Italy
Panaret – Arbëresh Easter bread shaped either into a circle or into two large braids and sprinkled with sesame seeds. It is adorned with red Easter eggs. The
Arbëreshë_people
Accommodation of magma in a host rock
used to describe the in situ inflation of the magma chamber of roughly spherical plutons. In this proposed model, the magma rises until it loses heat and
Pluton_emplacement
2020 American musical film and visual album by Beyoncé
with six braiders for three days to make it. There were 11 choreographers who worked on Black Is King. Stephen Ojo and Caleb Bonney of dance group AVO (Africa's
Black_Is_King
Clothing in Qatar
are rarely used in neighboring countries but are common in Qatar. After braiding the hair at the back of the head, the cap is secured with a bent metal
Qatari_clothing
Patterns of composition in Chinese characters
heart), 座 (zuò, seat), 旗 (qí, flag); Inner meaning and outer sound: 辮 (biàn, braid), 悶 (mèn, dull), 摹 (mó, imitation). Semantic-form characters (义记字; 義記字;
Chinese_character_structures
Theory of quantum gravity merging quantum mechanics and general relativity
arXiv:1204.5122 [gr-qc]. Bilson-Thompson, Sundance (2012). "Emergent Braided Matter of Quantum Geometry". Symmetry, Integrability and Geometry: Methods
Loop_quantum_gravity
Hill in Cheshire, United Kingdom
the south of Alderley represent material deposited in alluvial fan or braided river system. The finer sediments of the Wilmslow and Helsby Sandstone
Geology_of_Alderley_Edge
Textiles for medical and healthcare use
include many fiber types, yarns, fabrics, non-woven materials, woven, braided, as well as knitted fabrics. Physical and chemical alterations of fiber
Medical_textiles
Concept in chinese writing
(ill), phonetic 羊 (yáng). Inner meaning and outer sound, such as 辮 (biàn, braid), semantic 糸 (thread), phonetic 辡 (biàn); 悶 (mèn, dull), semantic 心 (heart)
Pianpang
Economist Gets Lunch: New Rules for Everyday Foodies. Penguin Publishing Group. p. pt50. ISBN 978-1-101-56166-9. Retrieved May 23, 2016. Raichlen, S. (2008)
List_of_street_foods
Traditional and contemporary cuisine of Quebec
meringue-based sweet. Mille-feuilles are a layered puff pastry. Croquignoles are braided, twisted or rectangular fried dough pastries. They may be found in rural
Cuisine_of_Quebec
Ensemble of states with an exactly specified total energy
contrast, are constrained to a 3 N {\displaystyle 3N} -dimensional (hyper-)spherical shell of radius 2 m E {\displaystyle {\sqrt {2mE}}} ; their contribution
Microcanonical_ensemble
Small explosive meant to produce noise
when they exploded also. Individual Mandarin crackers were most often braided into "strings" of varying lengths, which, when ignited, exploded in rapid
Firecracker
Historic site in Nakhchivan, Azerbaijan
elements of rectangular letters wrap around each other and become complex braids. The ground of these brick inscriptions represents a very finely crafted
Momine_Khatun_Mausoleum
German polymath and scholar (1777–1855)
Ostrowski 1920, pp. 1–18. Epple, Moritz (1998). "Orbits of asteroids, a braid, and the first link invariant". The Mathematical Intelligencer. 20 (1):
Carl_Friedrich_Gauss
"Sweet snacks from preserved fruit". Shine News. Shanghai United media Group. Retrieved 20 June 2017. "Rice Krispies Treats® Recipes - Rice Krispies®"
List_of_snack_foods
Specialized anatomy and physiology of bacteria
classification of bacteria. Typical examples include: coccus (circle or spherical) bacillus (rod-like) coccobacillus (between a sphere and a rod) spiral
Bacterial_cell_structure
Volcanic island in the Kermadec Islands
Prickett 2015, p. 513. Law of the Sea 2026. Nelson et al. 2018, p. 534. Braid & Bolstad 2019, p. 402. Veitch et al. 2004, p. 61. Song 2018, p. 253. Wright
Macauley_Island
Japanese anime television series
blue eyes and shoulder-length purple hair, mostly in two braids with multi-colored spherical beads at the ends, which shatter and have to be replaced
Wizard_Barristers
NASA mission to explore Mars via two rovers
the end of another bridle (tether), made of a nearly 20 m (66 ft) long braided Zylon. Zylon is a fiber material, similar to Kevlar, that is sewn in a
Mars_Exploration_Rover
Culinary traditions of Switzerland
honey as part of a leisurely breakfast or brunch. The name "Zopf" means "braid" in German, referring to the plaited form of the loaf. The bread's soft
Swiss_cuisine
Graduate-level textbooks in mathematics
9780691081540 82 Braids, Links, and Mapping Class Groups. Joan S. Birman 1975-02-01 237 978-0691081496 83 Automorphic Forms on Adele Groups. Stephen S. Gelbart
Annals_of_Mathematics_Studies
Нацпереліку нематеріальної культурної спадщини [The wedding ritual of "braiding dolia" has been included in the National Register of the Intangible Cultural
List of Intangible Cultural Heritage elements in Ukraine
List_of_Intangible_Cultural_Heritage_elements_in_Ukraine
Mathematics timeline
Fuchsian Groups. Cambridge University Press. p. ix. ISBN 9780521003506. Retrieved 17 January 2018. Platonov, Vladimir P. (2001) [1994], "Lie group", Encyclopedia
Timeline_of_manifolds
Time-telling device
white ivory, inlaid with black lacquer markings. The gnomons were black braided silk, linen or hemp string. With a knot or bead on the string as a nodus
Sundial
Coal and gas fired power stations in Nottinghamshire, England
location for the first nuclear fusion power plant to be built under the Spherical Tokamak for Energy Production (STEP) programme. The station is built on
West_Burton_power_stations
Load bearing cable connecting objects in space
2–3-millimeter (0.079–0.118 in) diameter tether with an outer layer of Spectra 1000 braid and a core of acrylic yarn. This satellite, the Tether Physics and Survivability
Space_tether
Geological Formation
suggested it reaches the Barremian. It is the uppermost unit of the Irhazer Group. Dinosaur remains & other vertebrates are among the fossils that have been
Tiourarén_Formation
Surgery to correct the deformities and defects of the auricle
likelier to protrude, but have a lesser incidence rate of granulomas, whereas braided sutures are unlikely to protrude, but have a greater incidence rate of
Otoplasty
Ethnographic region in Albania
tehri. They are short, with round buttons called sumbulla, and made with braid, tehri and kllapedan. Shokë e shallë: The shokë e shallë are known in English
Highlands_of_Gjakova
distance line laid in a cave for navigation. 2. Material: Small diameter braided synthetic cordage used for distance lines in cave diving . cave reel A
Glossary of underwater diving terminology: A–C
Glossary_of_underwater_diving_terminology:_A–C
Japanese light novel series
a reluctant member of a group founded by her older brother that has more than one name depending on the adaptation. This group studies and researches Cursed
C3_(novel_series)
19th-century look consisted of the combing of their hair and braiding them. They also wore red semi-spherical shaped hats which were embellished with tiny gold coins
Traditional clothing of Kosovo
Traditional_clothing_of_Kosovo
Pseudolines arranged largely to study arrangements of lines
similarities to braids, although without any need to keep track of which crosses atop the other, the crossings may be seen as elements of the Coxeter group. Two
Arrangement_of_pseudolines
Large Christmas tree near the White House in Washington, D.C.
just a third of the wattage of pre-1973 strings of lights), as well as braided gold-colored rope and large gold ornaments, were used. The Pageant of Peace
National Christmas Tree (United States)
National_Christmas_Tree_(United_States)
maximally symmetric braiding. symmetric sequence A symmetric sequence is a sequence of objects with actions of symmetric groups. It is categorically
Glossary_of_category_theory
Geologic formation in Poland
dominate and quartz pebbles association), can represent low-sinuosity braided channels. Another transgressive phase on this sequence led to the formation
Drzewica_Formation
Geologic formation in Poland and Germany
predominantly by high-sinuosity stream processes, transitioning from earlier braided and low-sinuosity stream systems. This evolution is attributed to climatic
Zagaje_Formation
Hydrogel made into a fibrous state
Stimuli-responsive hydrogel fibers can be used as actuators and soft robots. By braiding the hydrogel fiber together, the force of the single fiber can be magnified
Hydrogel_fiber
travel, tourism, insurance
SPHERICAL BRAID-GROUP
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SPHERICAL BRAID-GROUP
SPHERICAL BRAID-GROUP
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SPHERICAL BRAID-GROUP
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