The Lie algebra associated to the lower central series of a link group and Murasugi’s conjecture

Labute, John P.

doi:10.1090/S0002-9939-1990-1013973-7

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Browser Compatibility Info Help
ISSN 1088-6826(online) ISSN 0002-9939(print)

The Lie algebra associated to the lower central series of a link group and Murasugi's conjecture

Author: John P. Labute
Journal: Proc. Amer. Math. Soc. 109 (1990), 951-956
MSC: Primary 20F40; Secondary 57M25
MathSciNet review: 1013973
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The Chen-Milnor presentation can be used to determine the Lie Algebra associated to the lower central series of the fundamental group of a link in the -sphere ${S^3}$ in many interesting cases. We use this fact to obtain new and simpler proofs of unpublished results of Maeda on a conjecture of Murasugi in the sharpened form of Massey and Traldi.

[1] David J. Anick, Noncommutative graded algebras and their Hilbert series, J. Algebra 78 (1982), no. 1, 120–140. MR 677714 (84g:16001), http://dx.doi.org/10.1016/0021-8693(82)90104-1
[2] David J. Anick, Inert sets and the Lie algebra associated to a group, J. Algebra 111 (1987), no. 1, 154–165. MR 913201 (89d:20031), http://dx.doi.org/10.1016/0021-8693(87)90246-8
[3] N. Bourbaki, Éléments de mathématique. Fasc. XXXVII. Groupes et algèbres de Lie. Chapitre II: Algèbres de Lie libres. Chapitre III: Groupes de Lie, Hermann, Paris, 1972. Actualités Scientifiques et Industrielles, No. 1349. MR 0573068 (58 #28083a)
[4] Richard M. Hain, Iterated integrals, intersection theory and link groups, Topology 24 (1985), no. 1, 45–66. MR 790675 (86m:57008), http://dx.doi.org/10.1016/0040-9383(85)90044-8
[5] S. Halperin and J.-M. Lemaire, Suites inertes dans les algèbres de Lie graduées (“Autopsie d’un meurtre. II”), Math. Scand. 61 (1987), no. 1, 39–67 (French). MR 929396 (89e:55022)
[6] John P. Labute, Algèbres de Lie et pro-𝑝-groupes définis par une seule relation, Invent. Math. 4 (1967), 142–158 (French). MR 0218495 (36 #1581)
[7] John P. Labute, The determination of the Lie algebra associated to the lower central series of a group, Trans. Amer. Math. Soc. 288 (1985), no. 1, 51–57. MR 773046 (86b:20049), http://dx.doi.org/10.1090/S0002-9947-1985-0773046-8
[8] T. Maeda, Lower central series of link groups, Ph.D. thesis, Univ. of Toronto (1983), 1-104.
[9] William S. Massey and Lorenzo Traldi, On a conjecture of K. Murasugi, Pacific J. Math. 124 (1986), no. 1, 193–213. MR 850676 (87k:57008)
[10] John Milnor, Isotopy of links. Algebraic geometry and topology, A symposium in honor of S. Lefschetz, Princeton University Press, Princeton, N. J., 1957, pp. 280–306. MR 0092150 (19,1070c)

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|