This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
This is the same as taking the quotient of Fn with its commutator subgroup [Fn, Fn], which consists of all elements that can be written in the form αβα−1β−1, for some α, β ∈ Fn.
References
Allshouse MR, Thiffeault JL (2012) Detecting coherent structures using braids. Physica D 241(2):95–105
Artin E (1925) Theorie der zöpfe. Abh Math Semin Univ Hambg 4(1):47–72
Artin E (1947) Theory of braids. Ann Math 48(1):101–126
Bigelow SJ (1999) The Burau representation is not faithful for n = 5. Geom Topol 3:397–404
Bigelow SJ (2001) Braid groups are linear. J Am Math Soc 14(2):471–486
Birman JS (1975) Braids, links and mapping class groups. Annals of mathematics studies, vol 82. Princeton University Press, Princeton, NJ
Birman JS, Brendle TE (2005) Braids: A survey. In: Menasco W, Thistlethwaite M (eds) Handbook of Knot Theory. Elsevier, Amsterdam, pp 19–104
Boyland PL, Franks JM (1989) Lectures on dynamics of surface homeomorphisms. University of Warwick Preprint, notes by C. Carroll, J. Guaschi and T. Hall
Burau W (1936) Über Zopfgruppen und gleichsinnig verdrilte Verkettungen. Abh Math Semin Univ Hambg 11:171–178
Farb B, Margalit D (2011) A primer on mapping class groups. Princeton University Press, Princeton, NJ
Funar L, Kohno T (2013) On Burau’s representations at roots of unity. Geom Ded 169(1):145–163
Gambaudo JM, Ghys E (2005) Braids and signatures. Bulletin de la Société mathématique de France 133(4):541–579
Long DD, Paton M (1993) The Burau representation is not faithful for n ≥ 6. Topology 32:439–447
Moody JA (1991) The Burau representation of the braid group Bn is unfaithful for large n. Bull Am Math Soc 25:379–384
Rolfsen D (2003) New developments in the theory of Artin’s braid groups. Topol Appl 127(1-2):77–90
Venkataramana TN (2014) Image of the Burau representation at d-th roots of unity. Ann Math 179(3):1041–1083
Yeung M, Cohen-Steiner D, Desbrun M (2020) Material coherence from trajectories via Burau eigenanalysis of braids. Chaos 30:033122
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Thiffeault, JL. (2022). Braids. In: Braids and Dynamics. Frontiers in Applied Dynamical Systems: Reviews and Tutorials, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-031-04790-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-031-04790-9_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-04789-3
Online ISBN: 978-3-031-04790-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)