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On the linear representation of braid groups
Author:
D. D. Long
Journal:
Trans. Amer. Math. Soc. 311 (1989), 535-560
MSC:
Primary 20F36; Secondary 32B30, 57M25
MathSciNet review:
943606
Full-text PDF Free Access
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Abstract: We give a new derivative of the Burau and Gassner representations of the braid and pure braid groups. Various applications are explored.
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B. A. Epstein, Almost all subgroups of a Lie group are free,
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D. James, The representation theory of the symmetric groups,
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(80g:20019)
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Vaughan
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(N.S.) 12 (1985), no. 1, 103–111. MR 766964
(86e:57006), http://dx.doi.org/10.1090/S0273-0979-1985-15304-2
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F. R. Jones, Hecke algebra representations of braid groups and link
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no. 2, 335–388. MR 908150
(89c:46092), http://dx.doi.org/10.2307/1971403
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D.
D. Long, A note on the normal subgroups of mapping class
groups, Math. Proc. Cambridge Philos. Soc. 99 (1986),
no. 1, 79–87. MR 809501
(87c:57009), http://dx.doi.org/10.1017/S0305004100063957
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 -manifold groups into a compact Lie group, preprint.
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Wilhelm
Magnus, Rings of Fricke characters and automorphism groups of free
groups, Math. Z. 170 (1980), no. 1,
91–103. MR
558891 (81a:20043), http://dx.doi.org/10.1007/BF01214715
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D. Stasheff, Characteristic classes, Princeton University
Press, Princeton, N. J., 1974. Annals of Mathematics Studies, No. 76. MR 0440554
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M. Spivak, A comprehesive introduction to differential geometry, Publish or Perish.
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Craig
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- [1]
- J. Frank Adams, Lectures on Lie groups, Univ. of Chicago Press, 1969. MR 0252560 (40:5780)
- [2]
- J. Birman, Braids, links and mapping class groups, Ann. of Math. Studies, no. 82, Princeton Univ. Press, Princeton, N.J., 1975. MR 0375281 (51:11477)
- [3]
- -, On the Jones polynomial of closed
 -braids, Invent. Math. 81 (1985), 287-294. MR 799267 (86m:57006)
- [4]
- W. Burau, Uber Zopfgruppen und gleichsinnig verfrillte Verkettunger, Abh. Math. Sem. Hanischen Univ. 11 (1936), 171-178.
- [5]
- D. B. A. Epstein, Almost all subgroups of a Lie group are free, J. Algebra 19 (1971), 261-262. MR 0281776 (43:7491)
- [6]
- G. D. James, Representation theory of the symmetric groups, Lecture Notes in Math., vol. 682, Springer-Verlag, Berlin and New York. MR 513828 (80g:20019)
- [7]
- V. F. R. Jones, A polynomial invariant for knots via von Neuamnn algebras, Bull. Amer. Math. Soc. (N.S.) 12 (1985), 103-111. MR 766964 (86e:57006)
- [8]
- -, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. (2) 126 (1987), 335-388. MR 908150 (89c:46092)
- [9]
- D. D. Long, A note on the normal subgroups of mapping class groups, Math. Proc. Cambridge Philos. Soc. 99 (1986), 79-87. MR 809501 (87c:57009)
- [10]
- -, Representations of fibred -manifold groups into a compact Lie group, preprint.
- [11]
- W. Magnus, Rings of Fricke characters and automorphism groups of free groups, Math. Z. 170 (1980), 91-103. MR 558891 (81a:20043)
- [12]
- J. W. Milnor, Characteristic classes, Ann. of Math. Studies, no. 76, Princeton Univ. Press, Princeton, N.J., 1974. MR 0440554 (55:13428)
- [13]
- -, Morse theory, Ann. of Math. Studies, no. 51, Princeton Univ. Press, Princeton, N.J., 1963.
- [14]
- M. Spivak, A comprehesive introduction to differential geometry, Publish or Perish.
- [15]
- C. Squier, The Burau representation is unitary, Proc. Amer. Math. Soc. 90 (1984), 199-202. MR 727232 (85b:20056)
- [16]
- A. Weinstein, Lectures on symplectic manifolds, CBMS Regional Conf. Ser. Math., no. 29, Amer. Math. Soc., Providence, R.I., 1977; reprinted 1983. MR 0464312 (57:4244)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1989-0943606-3
PII:
S 0002-9947(1989)0943606-3
Article copyright:
© Copyright 1989 American Mathematical Society
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