Braid group (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Braid group" in English language version.

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mathscinet.ams.org

Boyland, Philip L.; Aref, Hassan; Stremler, Mark A. (2000), "Topological fluid mechanics of stirring" (PDF), Journal of Fluid Mechanics, 403 (1): 277–304, Bibcode:2000JFM...403..277B, doi:10.1017/S0022112099007107, hdl:2142/112556, MR 1742169, S2CID 47710742, archived from the original (PDF) on 26 July 2011
Gouillart, Emmanuelle; Thiffeault, Jean-Luc; Finn, Matthew D. (2006), "Topological mixing with ghost rods", Physical Review E, 73 (3): 036311, arXiv:nlin/0510075, Bibcode:2006PhRvE..73c6311G, doi:10.1103/PhysRevE.73.036311, MR 2231368, PMID 16605655, S2CID 7142834
Lambropoulou, Sofia; Rourke, Colin P. (1997), "Markov's theorem in 3-manifolds", Topology and Its Applications, 78 (1–2): 95–122, arXiv:math/0405498, doi:10.1016/S0166-8641(96)00151-4, MR 1465027, S2CID 14494095
Birman, Joan S. (1974), Braids, links, and mapping class groups, Annals of Mathematics Studies, vol. 82, Princeton, N.J.: Princeton University Press, ISBN 978-0-691-08149-6, MR 0375281
Fox, Ralph; Neuwirth, Lee (1962). "The braid groups". Mathematica Scandinavica. 10: 119–126. doi:10.7146/math.scand.a-10518. MR 0150755.
- Fabel, Paul (2005), "Completing Artin's braid group on infinitely many strands", Journal of Knot Theory and Its Ramifications, 14 (8): 979–991, arXiv:math/0201303, doi:10.1142/S0218216505004196, MR 2196643, S2CID 16998867
- Fuks, Dmitry B. (1970). "Cohomology of the braid group mod 2". Functional Analysis and Its Applications. 4 (2): 143–151. doi:10.1007/BF01094491. MR 0274463. S2CID 123442457.
- Arnol'd, Vladimir (1969). "The cohomology ring of the colored braid group" (PDF). Mat. Zametki. 5: 227–231. MR 0242196.

arxiv.org

Cohen, Daniel; Suciu, Alexander (1997). "The Braid Monodromy of Plane Algebraic Curves and Hyperplane Arrangements". Commentarii Mathematici Helvetici. 72 (2): 285–315. arXiv:alg-geom/9608001. doi:10.1007/s000140050017. S2CID 14502859.
Gouillart, Emmanuelle; Thiffeault, Jean-Luc; Finn, Matthew D. (2006), "Topological mixing with ghost rods", Physical Review E, 73 (3): 036311, arXiv:nlin/0510075, Bibcode:2006PhRvE..73c6311G, doi:10.1103/PhysRevE.73.036311, MR 2231368, PMID 16605655, S2CID 7142834
Lambropoulou, Sofia; Rourke, Colin P. (1997), "Markov's theorem in 3-manifolds", Topology and Its Applications, 78 (1–2): 95–122, arXiv:math/0405498, doi:10.1016/S0166-8641(96)00151-4, MR 1465027, S2CID 14494095
Birman, Joan; Brendle, tara (2004). "BRAIDS: A SURVEY". p. 1.2. arXiv:math/0409205.
Garber, David (2009). "Braid Group Cryptography". arXiv:0711.3941v2 [cs.CR].
Nayak, Chetan; Wilczek, Frank (1996), " $2 n$ Quasihole States Realize $2 n -1$ -Dimensional Spinor Braiding Statistics in Paired Quantum Hall States", Nuclear Physics B, 479 (3): 529–553, arXiv:cond-mat/9605145, Bibcode:1996NuPhB.479..529N, doi:10.1016/0550-3213(96)00430-0, S2CID 18726223 Some of Wilczek-Nayak's proposals subtly violate known physics; see the discussion Read, N. (2003), "Nonabelian braid statistics versus projective permutation statistics", Journal of Mathematical Physics, 44 (2): 558–563, arXiv:hep-th/0201240, Bibcode:2003JMP....44..558R, doi:10.1063/1.1530369, S2CID 119388336
- Fabel, Paul (2005), "Completing Artin's braid group on infinitely many strands", Journal of Knot Theory and Its Ramifications, 14 (8): 979–991, arXiv:math/0201303, doi:10.1142/S0218216505004196, MR 2196643, S2CID 16998867

doi.org

Cohen, Daniel; Suciu, Alexander (1997). "The Braid Monodromy of Plane Algebraic Curves and Hyperplane Arrangements". Commentarii Mathematici Helvetici. 72 (2): 285–315. arXiv:alg-geom/9608001. doi:10.1007/s000140050017. S2CID 14502859.
Boyland, Philip L.; Aref, Hassan; Stremler, Mark A. (2000), "Topological fluid mechanics of stirring" (PDF), Journal of Fluid Mechanics, 403 (1): 277–304, Bibcode:2000JFM...403..277B, doi:10.1017/S0022112099007107, hdl:2142/112556, MR 1742169, S2CID 47710742, archived from the original (PDF) on 26 July 2011
Gouillart, Emmanuelle; Thiffeault, Jean-Luc; Finn, Matthew D. (2006), "Topological mixing with ghost rods", Physical Review E, 73 (3): 036311, arXiv:nlin/0510075, Bibcode:2006PhRvE..73c6311G, doi:10.1103/PhysRevE.73.036311, MR 2231368, PMID 16605655, S2CID 7142834
Stremler, Mark A.; Ross, Shane D.; Grover, Piyush; Kumar, Pankaj (2011), "Topological chaos and periodic braiding of almost-cyclic sets", Physical Review Letters, 106 (11): 114101, Bibcode:2011PhRvL.106k4101S, doi:10.1103/PhysRevLett.106.114101, hdl:10919/24513, PMID 21469863
Lambropoulou, Sofia; Rourke, Colin P. (1997), "Markov's theorem in 3-manifolds", Topology and Its Applications, 78 (1–2): 95–122, arXiv:math/0405498, doi:10.1016/S0166-8641(96)00151-4, MR 1465027, S2CID 14494095
Magnus, Wilhelm (1974). "Braid groups: A survey". Proceedings of the Second International Conference on the Theory of Groups. Lecture Notes in Mathematics. Vol. 372. Springer. pp. 463–487. doi:10.1007/BFb0065203. ISBN 978-3-540-06845-7.
Artin, Emil (1947). "Theory of Braids". Annals of Mathematics. 48 (1): 101–126. doi:10.2307/1969218. JSTOR 1969218.
Fox, Ralph; Neuwirth, Lee (1962). "The braid groups". Mathematica Scandinavica. 10: 119–126. doi:10.7146/math.scand.a-10518. MR 0150755.
Nayak, Chetan; Wilczek, Frank (1996), " $2 n$ Quasihole States Realize $2 n -1$ -Dimensional Spinor Braiding Statistics in Paired Quantum Hall States", Nuclear Physics B, 479 (3): 529–553, arXiv:cond-mat/9605145, Bibcode:1996NuPhB.479..529N, doi:10.1016/0550-3213(96)00430-0, S2CID 18726223 Some of Wilczek-Nayak's proposals subtly violate known physics; see the discussion Read, N. (2003), "Nonabelian braid statistics versus projective permutation statistics", Journal of Mathematical Physics, 44 (2): 558–563, arXiv:hep-th/0201240, Bibcode:2003JMP....44..558R, doi:10.1063/1.1530369, S2CID 119388336
- Fabel, Paul (2005), "Completing Artin's braid group on infinitely many strands", Journal of Knot Theory and Its Ramifications, 14 (8): 979–991, arXiv:math/0201303, doi:10.1142/S0218216505004196, MR 2196643, S2CID 16998867
- Ghrist, Robert (1 December 2009). "Configuration Spaces, Braids, and Robotics". Braids. Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore. Vol. 19. World Scientific. pp. 263–304. doi:10.1142/9789814291415_0004. ISBN 9789814291408.
- Fuks, Dmitry B. (1970). "Cohomology of the braid group mod 2". Functional Analysis and Its Applications. 4 (2): 143–151. doi:10.1007/BF01094491. MR 0274463. S2CID 123442457.

handle.net

hdl.handle.net

Boyland, Philip L.; Aref, Hassan; Stremler, Mark A. (2000), "Topological fluid mechanics of stirring" (PDF), Journal of Fluid Mechanics, 403 (1): 277–304, Bibcode:2000JFM...403..277B, doi:10.1017/S0022112099007107, hdl:2142/112556, MR 1742169, S2CID 47710742, archived from the original (PDF) on 26 July 2011
Stremler, Mark A.; Ross, Shane D.; Grover, Piyush; Kumar, Pankaj (2011), "Topological chaos and periodic braiding of almost-cyclic sets", Physical Review Letters, 106 (11): 114101, Bibcode:2011PhRvL.106k4101S, doi:10.1103/PhysRevLett.106.114101, hdl:10919/24513, PMID 21469863

harvard.edu

ui.adsabs.harvard.edu

Boyland, Philip L.; Aref, Hassan; Stremler, Mark A. (2000), "Topological fluid mechanics of stirring" (PDF), Journal of Fluid Mechanics, 403 (1): 277–304, Bibcode:2000JFM...403..277B, doi:10.1017/S0022112099007107, hdl:2142/112556, MR 1742169, S2CID 47710742, archived from the original (PDF) on 26 July 2011
Gouillart, Emmanuelle; Thiffeault, Jean-Luc; Finn, Matthew D. (2006), "Topological mixing with ghost rods", Physical Review E, 73 (3): 036311, arXiv:nlin/0510075, Bibcode:2006PhRvE..73c6311G, doi:10.1103/PhysRevE.73.036311, MR 2231368, PMID 16605655, S2CID 7142834
Stremler, Mark A.; Ross, Shane D.; Grover, Piyush; Kumar, Pankaj (2011), "Topological chaos and periodic braiding of almost-cyclic sets", Physical Review Letters, 106 (11): 114101, Bibcode:2011PhRvL.106k4101S, doi:10.1103/PhysRevLett.106.114101, hdl:10919/24513, PMID 21469863
Nayak, Chetan; Wilczek, Frank (1996), " $2 n$ Quasihole States Realize $2 n -1$ -Dimensional Spinor Braiding Statistics in Paired Quantum Hall States", Nuclear Physics B, 479 (3): 529–553, arXiv:cond-mat/9605145, Bibcode:1996NuPhB.479..529N, doi:10.1016/0550-3213(96)00430-0, S2CID 18726223 Some of Wilczek-Nayak's proposals subtly violate known physics; see the discussion Read, N. (2003), "Nonabelian braid statistics versus projective permutation statistics", Journal of Mathematical Physics, 44 (2): 558–563, arXiv:hep-th/0201240, Bibcode:2003JMP....44..558R, doi:10.1063/1.1530369, S2CID 119388336

jstor.org

Artin, Emil (1947). "Theory of Braids". Annals of Mathematics. 48 (1): 101–126. doi:10.2307/1969218. JSTOR 1969218.

mathnet.ru

mi.mathnet.ru

Markov, Andrey (1935), "Über die freie Äquivalenz der geschlossenen Zöpfe", Recueil Mathématique de la Société Mathématique de Moscou (in German and Russian), 1: 73–78

nih.gov

pubmed.ncbi.nlm.nih.gov

Gouillart, Emmanuelle; Thiffeault, Jean-Luc; Finn, Matthew D. (2006), "Topological mixing with ghost rods", Physical Review E, 73 (3): 036311, arXiv:nlin/0510075, Bibcode:2006PhRvE..73c6311G, doi:10.1103/PhysRevE.73.036311, MR 2231368, PMID 16605655, S2CID 7142834
Stremler, Mark A.; Ross, Shane D.; Grover, Piyush; Kumar, Pankaj (2011), "Topological chaos and periodic braiding of almost-cyclic sets", Physical Review Letters, 106 (11): 114101, Bibcode:2011PhRvL.106k4101S, doi:10.1103/PhysRevLett.106.114101, hdl:10919/24513, PMID 21469863

pdmi.ras.ru

Arnol'd, Vladimir (1969). "The cohomology ring of the colored braid group" (PDF). Mat. Zametki. 5: 227–231. MR 0242196.

semanticscholar.org

api.semanticscholar.org

Cohen, Daniel; Suciu, Alexander (1997). "The Braid Monodromy of Plane Algebraic Curves and Hyperplane Arrangements". Commentarii Mathematici Helvetici. 72 (2): 285–315. arXiv:alg-geom/9608001. doi:10.1007/s000140050017. S2CID 14502859.
Boyland, Philip L.; Aref, Hassan; Stremler, Mark A. (2000), "Topological fluid mechanics of stirring" (PDF), Journal of Fluid Mechanics, 403 (1): 277–304, Bibcode:2000JFM...403..277B, doi:10.1017/S0022112099007107, hdl:2142/112556, MR 1742169, S2CID 47710742, archived from the original (PDF) on 26 July 2011
Gouillart, Emmanuelle; Thiffeault, Jean-Luc; Finn, Matthew D. (2006), "Topological mixing with ghost rods", Physical Review E, 73 (3): 036311, arXiv:nlin/0510075, Bibcode:2006PhRvE..73c6311G, doi:10.1103/PhysRevE.73.036311, MR 2231368, PMID 16605655, S2CID 7142834
Lambropoulou, Sofia; Rourke, Colin P. (1997), "Markov's theorem in 3-manifolds", Topology and Its Applications, 78 (1–2): 95–122, arXiv:math/0405498, doi:10.1016/S0166-8641(96)00151-4, MR 1465027, S2CID 14494095
Nayak, Chetan; Wilczek, Frank (1996), " $2 n$ Quasihole States Realize $2 n -1$ -Dimensional Spinor Braiding Statistics in Paired Quantum Hall States", Nuclear Physics B, 479 (3): 529–553, arXiv:cond-mat/9605145, Bibcode:1996NuPhB.479..529N, doi:10.1016/0550-3213(96)00430-0, S2CID 18726223 Some of Wilczek-Nayak's proposals subtly violate known physics; see the discussion Read, N. (2003), "Nonabelian braid statistics versus projective permutation statistics", Journal of Mathematical Physics, 44 (2): 558–563, arXiv:hep-th/0201240, Bibcode:2003JMP....44..558R, doi:10.1063/1.1530369, S2CID 119388336
- Fabel, Paul (2005), "Completing Artin's braid group on infinitely many strands", Journal of Knot Theory and Its Ramifications, 14 (8): 979–991, arXiv:math/0201303, doi:10.1142/S0218216505004196, MR 2196643, S2CID 16998867
- Fuks, Dmitry B. (1970). "Cohomology of the braid group mod 2". Functional Analysis and Its Applications. 4 (2): 143–151. doi:10.1007/BF01094491. MR 0274463. S2CID 123442457.

uchicago.edu

math.uchicago.edu

Lieber, Joshua. "Introduction to Braid Groups" (PDF). math.uchicago.edu. p. 4.1.

ufl.edu

math.ufl.edu

Boyland, Philip L.; Aref, Hassan; Stremler, Mark A. (2000), "Topological fluid mechanics of stirring" (PDF), Journal of Fluid Mechanics, 403 (1): 277–304, Bibcode:2000JFM...403..277B, doi:10.1017/S0022112099007107, hdl:2142/112556, MR 1742169, S2CID 47710742, archived from the original (PDF) on 26 July 2011

web.archive.org

Boyland, Philip L.; Aref, Hassan; Stremler, Mark A. (2000), "Topological fluid mechanics of stirring" (PDF), Journal of Fluid Mechanics, 403 (1): 277–304, Bibcode:2000JFM...403..277B, doi:10.1017/S0022112099007107, hdl:2142/112556, MR 1742169, S2CID 47710742, archived from the original (PDF) on 26 July 2011

wolfram.com

mathworld.wolfram.com

Weisstein, Eric. "Braid Group". Wolfram Mathworld.
Weisstein, Eric W. (August 2014). "Braid Index". MathWorld – A Wolfram Web Resource. Retrieved 6 August 2014.