Abstract
This lecture on classical knot and link groups concentrates - after some remarks on general properties - on representations of these groups and invariants derived from them. Metabelian and higher-step-metabelian representations are considered and homomorphisms into hyperbolic isometries.
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References
G. Burde and K. Murasugi, Links and Seifert fibre spaces, Duke Math. J. 37 (1970), 89–93
G. Burde, Darstellungen von Knotengruppen and eine Knoteninvariante, Abh. Math. Sem. Univ. Hamb. 35 (1970), 107–120
G. Burde, Ueber periodische Knoten, Arch. Math. 30 (1978), 487–492
G. Burde, SU(2)¡ªrepresentation spaces for two-bridge knot groups, Math. Ann. 288 (1990), 103–119
G. Burde, Knots and knot spaces, this volume
D. Cooper, M. Culler, H. Gillet, D.D. Long and P.B. Shalen, Plane curves associated to character varieties of 3-manifolds, preprint
M. Culler, McA. Gordon, J. Luecke and P.B. Shalen, Dehn surgery on knots,Ann. of Math. 125 (1987) 237–300
M. Culler, and P.B. Shalen, Varieties of group representations and splittings of 3-manifolds, Annals of Mathematics, 117 (1983), 109–146
R. Hartley, Metabelian representations of knot groups, Pacific J. Math. 82 (1979), 93–104
R. Hartley, Lifting group homomorphisms,Pacific J. Math. 105 (1983), 311–320
R. Hartley and K. Murasugi, Covering linkage invariants, Canad. J. Math. 29 (1977), 1312–1339
M. Heusener, Dar•stcllungsraeunle von Knotenyruppen, Dissertation Frankfurt/Main (1992)
M. Kervaire, Les noeds de dimensions sup¨¦rieures, Bull. Soc. Math. France 93 (1965), 225–271
W. Magnus and A. Peluso, On knot groups, Commun. Pure Appl. Math. 20 (1967), 749–770
K. Murasugi, Nilpotent coverings of links and Milnor’s invariant, Proc. Sussex Conf. Low-dim.Top. (1982)
K. Reidemeister, Knoten and Verkettungen,Math. Z. 29 (1929), 713–729
K. Reidemeister, Knotentheorie, Ergehn. Math. Grenzgeb. Bd. 1 (1932)
R. Riley,.Algebra for Keckoid groups, preprint (1991)
S. Rosebrock, On the realization of IVirtinger presentations as knot groups, preprint.J.W.Goethe-Universitaet Frankfurt/Main
H. Seifert. (rebel. das Geschlecht von Knoten. Math. Ann. 110 (1934). 371–592
Z. Sela. The conjugacy problem for knot groups. preprint
H.F. Trotter, Non-invertible knots exist. Topology 2 (1964), 341–358
F. Waldhausen, The word problem in fundamental groups of sufficiently large irreducible 3-manifolds, Ann. of Math. 88 (1968), 272–280
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© 1993 Springer Science+Business Media Dordrecht
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Burde, G. (1993). Knot Groups. In: Bozhüyük, M.E. (eds) Topics in Knot Theory. NATO ASI Series, vol 399. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1695-4_3
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DOI: https://doi.org/10.1007/978-94-011-1695-4_3
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