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Congruence subgroups of braid groups
Tara E. Brendle1
1 Tara E. Brendle, School of Mathematics & Statistics, University Place, University of Glasgow, G12 8SQ
Winter Braids Lecture Notes, Volume 5 (2018), Talk no. 3, 26 p.
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These notes are based on a mini-course given at CIRM in February 2018 as part of the workshop Winter Braids VIII.

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Published online: 2020-06-29
DOI: 10.5802/wbln.23
Author's affiliations:
Tara E. Brendle 1

1 Tara E. Brendle, School of Mathematics & Statistics, University Place, University of Glasgow, G12 8SQ
  • BibTeX
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     title = {Congruence subgroups of braid groups},
     journal = {Winter Braids Lecture Notes},
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     publisher = {Winter Braids School},
     volume = {5},
     year = {2018},
     doi = {10.5802/wbln.23},
     language = {en},
     url = {https://wbln.centre-mersenne.org/articles/10.5802/wbln.23/}
}
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Tara E. Brendle. Congruence subgroups of braid groups. Winter Braids Lecture Notes, Volume 5 (2018), Talk no. 3, 26 p. doi : 10.5802/wbln.23. https://wbln.centre-mersenne.org/articles/10.5802/wbln.23/
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[1] Norbert A’Campo Tresses, monodromie et le groupe symplectique, Comment. Math. Helv., Volume 54 (1979) no. 2, pp. 318-327 | Article | MR: 535062 | Zbl: 0441.32004

[2] Jessica Appel; Wade Bloomquist; Katie Gravel; Annie Holden On Congruence Subgroups of the Braid Group (https://people.math.gatech.edu/~dmargalit7/reu.shtml/Braided_Poster.pdf)

[3] V. I. Arnol’d A remark on the branching of hyperelliptic integrals as functions of the parameters, Funkcional. Anal. i Priložen., Volume 2 (1968) no. 3, pp. 1-3 | MR: 0244266 | Zbl: 0192.58201

[4] E. Artin Theory of braids, Ann. of Math. (2), Volume 48 (1947), pp. 101-126 | Article | MR: 0019087 | Zbl: 0030.17703

[5] Emil Artin Theorie der Zöpfe, Abh. Math. Sem. Univ. Hamburg, Volume 4 (1925) no. 1, pp. 47-72 | Article | MR: 3069440 | Zbl: 51.0450.01

[6] Joachim Assion Einige endliche Faktorgruppen der Zopfgruppen, Math. Z., Volume 163 (1978) no. 3, pp. 291-302 | Article | MR: 513734 | Zbl: 0407.20030

[7] Stephen J. Bigelow; Ryan D. Budney The mapping class group of a genus two surface is linear, Algebr. Geom. Topol., Volume 1 (2001), pp. 699-708 | Article | MR: 1875613 | Zbl: 0999.57020

[8] Joan S. Birman On Siegel’s modular group, Math. Ann., Volume 191 (1971), pp. 59-68 | Article | MR: 0280606 | Zbl: 0208.10601

[9] Joan S. Birman Braids, links, and mapping class groups, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974, ix+228 pages (Annals of Mathematics Studies, No. 82) | MR: 0375281 | Zbl: 0297.57001

[10] Joan S. Birman; Hugh M. Hilden On isotopies of homeomorphisms of Riemann surfaces, Ann. of Math. (2), Volume 97 (1973), pp. 424-439 https://doi-org.prx.library.gatech.edu/10.2307/1970830 | Article | MR: 0325959 | Zbl: 0237.57001

[11] Tara Brendle; Dan Margalit; Andrew Putman Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t=-1, Invent. Math., Volume 200 (2015) no. 1, pp. 263-310 | Article | MR: 3323579 | Zbl: 1328.57021

[12] Tara E. Brendle; Dan Margalit Corrigendum to: The level four braid group (Preprint in preparation.)

[13] Tara E. Brendle; Dan Margalit Point pushing, homology, and the hyperelliptic involution, Michigan Math. J., Volume 62 (2013) no. 3, pp. 451-473 | Article | MR: 3102525 | Zbl: 1279.57013

[14] Tara E. Brendle; Dan Margalit The level four braid group, J. Reine Angew. Math., Volume 735 (2018), pp. 249-264 | Article | MR: 3757477 | Zbl: 06836109

[15] F. R. Cohen; J. Wu On braid groups and homotopy groups, Groups, homotopy and configuration spaces (Geom. Topol. Monogr.) Volume 13, Geom. Topol. Publ., Coventry, 2008, pp. 169-193 | Article | MR: 2508205 | Zbl: 1167.20022

[16] Max Dehn Papers on group theory and topology, Springer-Verlag, New York, 1987, viii+396 pages (Translated from the German and with introductions and an appendix by John Stillwell, With an appendix by Otto Schreier) | Article | MR: 881797 | Zbl: 1264.01046

[17] Steven Diaz; Ron Donagi; David Harbater Every curve is a Hurwitz space, Duke Math. J., Volume 59 (1989) no. 3, pp. 737-746 https://doi-org.ezproxy.lib.gla.ac.uk/10.1215/S0012-7094-89-05933-4 | Article | MR: 1046746 | Zbl: 0712.14013

[18] Benson Farb; Dan Margalit A primer on mapping class groups, Princeton Mathematical Series, Volume 49, Princeton University Press, Princeton, NJ, 2012, xiv+472 pages | MR: 2850125 | Zbl: 1245.57002

[19] Neil Fullarton; Andrew Putman The high-dimensional cohomology of the moduli space of curves with level structures, J. Eur. Math. Soc. (to appear) | Zbl: 07198108

[20] Neil J. Fullarton A generating set for the palindromic Torelli group, Algebr. Geom. Topol., Volume 15 (2015) no. 6, pp. 3535-3567 | Article | MR: 3450770 | Zbl: 1368.20026

[21] Jean-Marc Gambaudo; Étienne Ghys Braids and signatures, Bull. Soc. Math. France, Volume 133 (2005) no. 4, pp. 541-579 | Article | Numdam | MR: 2233695 | Zbl: 1103.57001

[22] Edna K. Grossman On the residual finiteness of certain mapping class groups, J. London Math. Soc. (2), Volume 9 (1974/75), pp. 160-164 | Article | MR: 0405423 | Zbl: 0292.20032

[23] Richard Hain Finiteness and Torelli spaces, Problems on mapping class groups and related topics (Proc. Sympos. Pure Math.) Volume 74, Amer. Math. Soc., Providence, RI, 2006, pp. 57-70 | Article | MR: 2264131 | Zbl: 1222.14014

[24] John L. Harer The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math., Volume 84 (1986) no. 1, pp. 157-176 | Article | MR: 830043 | Zbl: 0592.57009

[25] Stephen P. Humphries Generators for the mapping class group, Topology of low-dimensional manifolds (Proc. Second Sussex Conf., Chelwood Gate, 1977) (Lecture Notes in Math.) Volume 722, Springer, Berlin, 1979, pp. 44-47 | Article | MR: 547453 | Zbl: 0732.57004

[26] N. V. Ivanov Residual finiteness of modular Teichmüller groups, Sibirsk. Mat. Zh., Volume 32 (1991) no. 1, p. 182-185, 222 | Article | MR: 1112097

[27] Nikolai V. Ivanov Subgroups of Teichmüller modular groups, Translations of Mathematical Monographs, Volume 115, American Mathematical Society, Providence, RI, 1992, xii+127 pages (Translated from the Russian by E. J. F. Primrose and revised by the author) | MR: 1195787

[28] Nikolai V. Ivanov Automorphism of complexes of curves and of Teichmüller spaces, Internat. Math. Res. Notices, Volume 1997 (1997) no. 14, pp. 651-666 | Article | MR: 1460387

[29] Dennis Johnson An abelian quotient of the mapping class group ℐ g , Math. Ann., Volume 249 (1980) no. 3, pp. 225-242 https://doi-org.prx.library.gatech.edu/10.1007/BF01363897 | Article | MR: 579103 | Zbl: 0409.57009

[30] Dennis Johnson The structure of the Torelli group. I. A finite set of generators for ℐ, Ann. of Math. (2), Volume 118 (1983) no. 3, pp. 423-442 https://doi-org.prx.library.gatech.edu/10.2307/2006977 | Article | MR: 727699 | Zbl: 0549.57006

[31] Dennis Johnson The structure of the Torelli group. II. A characterization of the group generated by twists on bounding curves, Topology, Volume 24 (1985) no. 2, pp. 113-126 https://doi-org.prx.library.gatech.edu/10.1016/0040-9383(85)90049-7 | Article | MR: 793178 | Zbl: 0571.57009

[32] JSE The image of the point-pushing group in the hyperelliptic representation of the braid group (MathOverflow, https://mathoverflow.net/questions/105048/the-image-of-the-point-pushing-group-in-the-hyperelliptic-representation-of-the)

[33] Kevin Kordek; Dan Margalit Representation stability in the level 4 braid group (arXiv:1903.03119)

[34] Mustafa Korkmaz Automorphisms of complexes of curves on punctured spheres and on punctured tori, Topology Appl., Volume 95 (1999) no. 2, pp. 85-111 | Article | MR: 1696431 | Zbl: 0926.57012

[35] Catherine Labruère; Luis Paris Presentations for the punctured mapping class groups in terms of Artin groups, Algebr. Geom. Topol., Volume 1 (2001), pp. 73-114 https://doi-org.ezproxy.lib.gla.ac.uk/10.2140/agt.2001.1.73 | Article | MR: 1805936 | Zbl: 0962.57008

[36] Feng Luo Automorphisms of the complex of curves, Topology, Volume 39 (2000) no. 2, pp. 283-298 | Article | MR: 1722024 | Zbl: 0951.32012

[37] Dan Margalit; Rebecca Winarski BIrman-Hilden theory, Celebratio Mathematica (To appear)

[38] D. B. McReynolds The congruence subgroup problem for pure braid groups: Thurston’s proof, New York J. Math., Volume 18 (2012), pp. 925-942 http://nyjm.albany.edu:8000/j/2012/18_925.html | MR: 3007206 | Zbl: 1331.20046

[39] J. Mennicke Zur Theorie der Siegelschen Modulgruppe, Math. Ann., Volume 159 (1965), pp. 115-129 | Article | MR: 181676 | Zbl: 0134.26502

[40] Geoffrey Mess The Torelli groups for genus 2 and 3 surfaces, Topology, Volume 31 (1992) no. 4, pp. 775-790 https://doi-org.prx.library.gatech.edu/10.1016/0040-9383(92)90008-6 | Article | MR: 1191379 | Zbl: 0772.57025

[41] Takayuki Morifuji On Meyer’s function of hyperelliptic mapping class groups, J. Math. Soc. Japan, Volume 55 (2003) no. 1, pp. 117-129 | Article | MR: 1939188 | Zbl: 1031.57017

[42] Morris Newman Integral matrices, Academic Press, New York-London, 1972, xvii+224 pages (Pure and Applied Mathematics, Vol. 45) | MR: 0340283 | Zbl: 0254.15009

[43] Jerome Powell Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc., Volume 68 (1978) no. 3, pp. 347-350 | Article | MR: 0494115 | Zbl: 0391.57009

[44] Andrew Putman Lectures on the Torelli group (https://www3.nd.edu/ andyp/teaching/2014SpringMath541/)

[45] Andrew Putman The Torelli group and congruence subgroups of the mapping class group (https://www3.nd.edu/ andyp/notes/)

[46] Andrew Putman Cutting and pasting in the Torelli group, Geom. Topol., Volume 11 (2007), pp. 829-865 | Article | MR: 2302503 | Zbl: 1157.57010

[47] Andrew Putman An infinite presentation of the Torelli group, Geom. Funct. Anal., Volume 19 (2009) no. 2, pp. 591-643 | Article | MR: 2545251 | Zbl: 1178.57001

[48] Andrew Putman Obtaining presentations from group actions without making choices, Algebr. Geom. Topol., Volume 11 (2011) no. 3, pp. 1737-1766 | Article | MR: 2821439 | Zbl: 1247.20041

[49] M. S. Raghunathan The congruence subgroup problem, Proc. Indian Acad. Sci. Math. Sci., Volume 114 (2004) no. 4, pp. 299-308 | Article | MR: 2067695 | Zbl: 1086.20024

[50] Dale Rolfsen Knots and links, Publish or Perish, Inc., Berkeley, Calif., 1976, ix+439 pages (Mathematics Lecture Series, No. 7) | MR: 0515288 | Zbl: 0339.55004

[51] H. L. Royden Automorphisms and isometries of Teichmüller space, Advances in the Theory of Riemann Surfaces (Proc. Conf., Stony Brook, N.Y., 1969) (Ann. of Math. Studies) Volume 66 (1971), pp. 369-383 | Article | MR: 0288254 | Zbl: 0218.32011

[52] Nancy Scherich Classification of the real discrete specialisations of the Burau representation of B3, Math. Proc. Cambridge Philos. Soc., Volume 168 (2020) no. 2, pp. 295-304 https://doi-org.ezproxy.lib.gla.ac.uk/10.1017/s0305004118000683 | Article | MR: 4064106 | Zbl: 07167596

[53] Craig C. Squier The Burau representation is unitary, Proc. Amer. Math. Soc., Volume 90 (1984) no. 2, pp. 199-202 | Article | MR: 727232 | Zbl: 0542.20022

[54] Charalampos Stylianakis Congruence subgroups of braid groups, Internat. J. Algebra Comput., Volume 28 (2018) no. 2, pp. 345-364 | Article | MR: 3786423 | Zbl: 1396.20037

[55] J. G. Sunday Presentations of the groups SL (2,m) and PSL (2,m), Canadian J. Math., Volume 24 (1972), pp. 1129-1131 | Article | MR: 311782 | Zbl: 0253.20051

[56] Vladimir Turaev Faithful linear representations of the braid groups, Astérisque (2002) no. 276, pp. 389-409 (Séminaire Bourbaki, Vol. 1999/2000) | Numdam | MR: 1886767 | Zbl: 1050.20026

[57] Bronislaw Wajnryb A braidlike presentation of Sp (n,p), Israel J. Math., Volume 76 (1991) no. 3, pp. 265-288 | Article | MR: 1177345 | Zbl: 0791.20037

[58] J.-K. Yu Toward a proof of the Cohen-Lenstra conjecture in the function field case (1996) (Preprint.)

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