Bulletin of the American Mathematical Society

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Book Information:

Authors: G. Burde and H. Zieschang
Title: Knots
Additional book information: de Gruyter Stud. Math., vol. 5, Walter de Gruyter, New York, 2003, xii+559 pp., ISBN 3-11-017005-1, $69.95$

Author: Jonathan Hillman
Title: Algebraic invariants of links
Additional book information: Series on Knots and Everything, Volume 32, World Scientific Co. Pte. Ltd., Singapore, 2002, xii+305 pp., ISBN 789812-381545, $42.00$

[A20]

J.W. Alexander, Note on Riemann spaces, Bull. Amer. Math. Soc. 26 (1920), 370-372.

[A25]

E. Artin, Zur Isotopie zweidimensionaler Flächen in , Abh. Math. Sem. Univ. Hamburg 4 (1925), 174-177.

[A88]

M.F. Atiyah, New invariants of and dimensional manifolds, Sympos. on the Math. Heritage of Hermann Weyl (R.O. Wells, ed.), 1987, Amer. Math. Soc., Providence, RI, 1988, 285-299. MR 0974342

[CS98]

J.S. Carter and M. Saito, Knotted Surfaces and Their Diagrams, Mathematical Surveys and Monographs 55, Amer. Math. Soc., Providence, RI, 1998. MR 1487374

[CG75]

A. Casson and C. McA. Gordon, Cobordism of classical knots, in A la Recherche de la Topologie Perdue (Guillou and Marin, eds.), Progr. Math. 62, 1986, 181-199; originally published as Orsay Preprint, 1975. MR 0900243

[C90]

T.D. Cochran, Derivatives of links: Milnor's concordance invariants and Massey's products, Memoirs of the Amer. Math. Soc. 84, Amer. Math. Soc., Providence, RI, 1990. MR 1042041

[COT03]

T.D. Cochran, K.E. Orr and P. Teichner, Knot concordance, Whitney towers and -signatures, Annals of Math. 157 (2003), 433-519.

[E99]

M. Epple, Geometric aspects in the development of knot theory, in History of Topology (I.M. James, ed.), North-Holland, Amsterdam, 1999, 301-358. MR 1674917

[F75]

M. Farber, Linking coefficients and two-dimensional knots, Soviet Math. Dokl. 16 (1975), 647-650. MR 0400246

[FM66]

R.H. Fox and J.W. Milnor, Singularities of -spheres in -space and cobordism of knots, Osaka Math. J. 3 (1960), 257-267. MR 0211392

[G33]

C.F. Gauss, Werke, 6 Volumes, Königliche Gesellschaft der Wissenschaften, Göttingen, 1863-1933, Vol. VI, 106-118.

[G76]

C.H. Giffen, F-isotopy and I-equivalence, unpublished manuscript, Univ. of Virginia, 1976.

[G83]

P.M. Gilmer, Slice knots in , Quart. J. Math. 34 (1983), 305-322. MR 0711523

[G93]

P.M. Gilmer, Classical knot and link concordance, Comment. Math. Helv. 69 (1993), 1-19. MR 1201199

[G79]

C. McA. Gordon, Some aspects of classical knot theory, in Knot Theory, Proceedings, Plans-sur-Bex, Switzerland 1977 (J.C. Haussmann, ed.), Lecture Notes in Math. 685, Springer-Verlag, Berlin, 1979, 1-60. MR 0521730

[G72]

M. Gutierrez, On knot modules, Invent. Math. 17 (972), 329-335. MR 0321103

[HL90]

N. Habegger and X.S. Lin, The classification of links up to link-homotopy, J. Amer. Math. Soc. 3 (1990), 389-419. MR 1026062

[H61]

W. Haken, Theorie der Normalflächen, Acta Mathematica 105 (1961), 245-375. MR 0141106

[H93]

J. Hughes, Structured groups and link-homotopy, J. Knot Theory and its Ramifications 2 (1993), 37-63. MR 1209318

[H98]

J. Hughes, Distinguishing link-homotopy classes by pre-peripheral structures, J. Knot Theory and its Ramifications 7 (1998), 925-944. MR 1654653

[K87]

L.H. Kauffman, State models and the Jones polynomial, Topology 26 (1987), 395-407. MR 0899057

[K64]

M. Kervaire, Les noeuds de dimension supérieure, Bull. Soc. Math. de France 93 1965, 225-271. MR 0189052

[K65]

M. Kervaire, On higher-dimensional knots, in Differential and Combinatorial Topology (S. Cairn, ed.), Princeton Univ. Press, 1965, 105-120. MR 0178475

[KW79]

M. Kervaire and C. Weber, A survey of multidimensional knots, in Knot Theory, Proceedings, Plans-sur-Bex, Switzerland 1977 (J.C. Haussmann, ed.), Lecture Notes in Math. 685, Springer-Verlag, Berlin, 1979, 61-134. MR 0521731

[K97]

R. Kirby, Problems in low-dimensional topology (R. Kirby, ed.), AMS/IP Stud. Adv. Math., 2.2, Geometric topology, Athens, GA, 1993, 33-473, Amer. Math. Soc., Providence, RI, 1997.

[KL99]

P. Kirk and C. Livingston, Twisted Alexander invariants, Reidemeister torsion, and Casson-Gordon invariants, Topology 38 (1999), 635-661. MR 1670420

[K11]

C.G. Knott, Life and Scientific Work of Peter Guthrie Tait, Cambridge Univ. Press, Cambridge, 1911.

[L00]

C. Letsche, A new slicing obstruction using the eta invariant, Proc. Cambridge Philos. Soc. 128 (2000), 301-319. MR 1735303

[L69]

J. Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969), 229-244. MR 0246314

[L77]

J. Levine, Knot modules: I, Trans. Amer. Math. Soc. 229 (1977), 1-50. MR 0461518

[L88]

J. Levine, An approach to homotopy classification of links, Trans. Amer. Math. Soc. 306 (1988), 361-387. MR 0927695

[LO03]

J. Levine and K. Orr, A survey of applicatioons of surgery to knot and link theory, in Surveys on Surgery Theory, Vol. 1 (S. Cappell, A. Ranicki, J. Rosenberg, eds.), Ann. of Math. Studies 145, Princeton, NJ, 2003, 345-364. MR 1747541

[L48]

J.B. Listing, Vorstudien zur Topologie, Göttingen Studien 2 (1848), 811-875; separately published: Vandenhoeck und Ruprecht, Göttingen, 1848.

[L03]

C. Livingston, A survey of classical knot concordance, preprint, arXiv:math.GT/0307077, 2003.

[M91]

J.C. Maxwell, A Treatise on Electricity and Magnetism, 3rd ed., Clarendon Press, Oxford, 1891; reprinted by Dover Publications, NY, 1954. MR 16:99b

[MT93]

W. Menasco and M.B. Thistlethwaite, The classification of alternating links, Annals of Math. 138 (1993), 113-171. MR 1230928

[M54]

J.W. Milnor, Link groups, Annals of Math. 59 (1954), 177-195. MR 17:70e

[M57]

J.W. Milnor, Isotopy of links, in Algebraic Geometry and Topology (Fox, Spencer and Tucker, eds.), Princeton Univ. Press, 1957, 280-306. MR 19:1070c

[M87]

K. Murasugi, The Jones polynomial and classical conjectures in knot theory, Topology 26 (1987), 187-194. MR 0895570

[R32]

K. Reidemeister, Knotentheorie, Springer, Berlin, 1932.

[R93]

D. Roseman, Twisting and turning in four dimensions, video made at the Geometry Center, 1993.

[S66]

N.F. Smythe, Boundary links in Topology Seminar, Wisconsin 1965 (R.H. Bing, ed.), Annals of Math. Study 60, Princeton Univ. Press, Princeton, 1966, 69-72. MR 0202100

[S77]

N. Stoltzfus, Unraveling the integral knot concordance group, Memoirs of the Amer. Math. Soc. 192, Amer. Math. Soc., Providence, RI, 1977. MR 0467764

[T76]

P.G. Tait, Recent Advances in Physical Sciences, 2nd ed., Macmillan and Co., London, 1876, 294.

[T77]

P.G. Tait, On knots, Trans. of the RSE 28 (1877), 145-190; reprinted in: P.G. Tait, Collected Scientific Papers, Vol. I, Cambridge Univ. Press, Cambridge, 1898, 273-317.

[T84]

P.G. Tait, On knots. Part II, Trans. RSE 32 (1884-1885), 327-339; reprinted in: P.G. Tait, Collected Scientific Papers, Vol. II, Cambridge Univ. Press, Cambridge, 1898, 318-333.

[T84]

P.G. Tait, On knots. Part III, Trans. RSE 32 (1884-1885), 493-506; reprinted in: P.G. Tait, Collected Scientific Papers, Vol. II, Cambridge Univ. Press, Cambridge, 1898, 335-347.

[T85]

M.B. Thistlethwaite, Knot tabulations and related results, in Aspects of Topology, LMS Lecture Series 93, Cambridge Univ. Press, Cambridge, 1985, 1-76. MR 0787823

[T87]

M.B. Thistlethwaite, A spanning tree expansion of the Jones polynomial, Topology 26 (1987), 297-309. MR 0899051

[W68]

F. Waldhausen, On irreducible -manifolds which are sufficiently large, Annals of Math. 87 (1968), 56-88. MR 0224099

[W87]

W. Whitten, Knot complements and groups, Topology 26 (1987), 41-44. MR 0880506

[W89]

E. Witten, Some geometric applications of quantum field theory, I, A.M.P. Congress, Swansea, 1988 (I. Davies, B. Simon and A. Truman, eds.), Institute of Physics, College Park, MD, 1989.

[W89]

E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), 351-399. MR 0990772

[A20]

J.W. Alexander, Note on Riemann spaces, Bull. Amer. Math. Soc. 26 (1920), 370-372.

[A25]

E. Artin, Zur Isotopie zweidimensionaler Flächen in , Abh. Math. Sem. Univ. Hamburg 4 (1925), 174-177.

[A88]

M.F. Atiyah, New invariants of and dimensional manifolds, Sympos. on the Math. Heritage of Hermann Weyl (R.O. Wells, ed.), 1987, Amer. Math. Soc., Providence, RI, 1988, 285-299. MR 0974342

[CS98]

J.S. Carter and M. Saito, Knotted Surfaces and Their Diagrams, Mathematical Surveys and Monographs 55, Amer. Math. Soc., Providence, RI, 1998. MR 1487374

[CG75]

A. Casson and C. McA. Gordon, Cobordism of classical knots, in A la Recherche de la Topologie Perdue (Guillou and Marin, eds.), Progr. Math. 62, 1986, 181-199; originally published as Orsay Preprint, 1975. MR 0900243

[C90]

T.D. Cochran, Derivatives of links: Milnor's concordance invariants and Massey's products, Memoirs of the Amer. Math. Soc. 84, Amer. Math. Soc., Providence, RI, 1990. MR 1042041

[COT03]

T.D. Cochran, K.E. Orr and P. Teichner, Knot concordance, Whitney towers and -signatures, Annals of Math. 157 (2003), 433-519.

[E99]

M. Epple, Geometric aspects in the development of knot theory, in History of Topology (I.M. James, ed.), North-Holland, Amsterdam, 1999, 301-358. MR 1674917

[F75]

M. Farber, Linking coefficients and two-dimensional knots, Soviet Math. Dokl. 16 (1975), 647-650. MR 0400246

[FM66]

R.H. Fox and J.W. Milnor, Singularities of -spheres in -space and cobordism of knots, Osaka Math. J. 3 (1960), 257-267. MR 0211392

[G33]

C.F. Gauss, Werke, 6 Volumes, Königliche Gesellschaft der Wissenschaften, Göttingen, 1863-1933, Vol. VI, 106-118.

[G76]

C.H. Giffen, F-isotopy and I-equivalence, unpublished manuscript, Univ. of Virginia, 1976.

[G83]

P.M. Gilmer, Slice knots in , Quart. J. Math. 34 (1983), 305-322. MR 0711523

[G93]

P.M. Gilmer, Classical knot and link concordance, Comment. Math. Helv. 69 (1993), 1-19. MR 1201199

[G79]

C. McA. Gordon, Some aspects of classical knot theory, in Knot Theory, Proceedings, Plans-sur-Bex, Switzerland 1977 (J.C. Haussmann, ed.), Lecture Notes in Math. 685, Springer-Verlag, Berlin, 1979, 1-60. MR 0521730

[G72]

M. Gutierrez, On knot modules, Invent. Math. 17 (972), 329-335. MR 0321103

[HL90]

N. Habegger and X.S. Lin, The classification of links up to link-homotopy, J. Amer. Math. Soc. 3 (1990), 389-419. MR 1026062

[H61]

W. Haken, Theorie der Normalflächen, Acta Mathematica 105 (1961), 245-375. MR 0141106

[H93]

J. Hughes, Structured groups and link-homotopy, J. Knot Theory and its Ramifications 2 (1993), 37-63. MR 1209318

[H98]

J. Hughes, Distinguishing link-homotopy classes by pre-peripheral structures, J. Knot Theory and its Ramifications 7 (1998), 925-944. MR 1654653

[K87]

L.H. Kauffman, State models and the Jones polynomial, Topology 26 (1987), 395-407. MR 0899057

[K64]

M. Kervaire, Les noeuds de dimension supérieure, Bull. Soc. Math. de France 93 1965, 225-271. MR 0189052

[K65]

M. Kervaire, On higher-dimensional knots, in Differential and Combinatorial Topology (S. Cairn, ed.), Princeton Univ. Press, 1965, 105-120. MR 0178475

[KW79]

M. Kervaire and C. Weber, A survey of multidimensional knots, in Knot Theory, Proceedings, Plans-sur-Bex, Switzerland 1977 (J.C. Haussmann, ed.), Lecture Notes in Math. 685, Springer-Verlag, Berlin, 1979, 61-134. MR 0521731

[K97]

R. Kirby, Problems in low-dimensional topology (R. Kirby, ed.), AMS/IP Stud. Adv. Math., 2.2, Geometric topology, Athens, GA, 1993, 33-473, Amer. Math. Soc., Providence, RI, 1997.

[KL99]

P. Kirk and C. Livingston, Twisted Alexander invariants, Reidemeister torsion, and Casson-Gordon invariants, Topology 38 (1999), 635-661. MR 1670420

[K11]

C.G. Knott, Life and Scientific Work of Peter Guthrie Tait, Cambridge Univ. Press, Cambridge, 1911.

[L00]

C. Letsche, A new slicing obstruction using the eta invariant, Proc. Cambridge Philos. Soc. 128 (2000), 301-319. MR 1735303

[L69]

J. Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969), 229-244. MR 0246314

[L77]

J. Levine, Knot modules: I, Trans. Amer. Math. Soc. 229 (1977), 1-50. MR 0461518

[L88]

J. Levine, An approach to homotopy classification of links, Trans. Amer. Math. Soc. 306 (1988), 361-387. MR 0927695

[LO03]

J. Levine and K. Orr, A survey of applicatioons of surgery to knot and link theory, in Surveys on Surgery Theory, Vol. 1 (S. Cappell, A. Ranicki, J. Rosenberg, eds.), Ann. of Math. Studies 145, Princeton, NJ, 2003, 345-364. MR 1747541

[L48]

J.B. Listing, Vorstudien zur Topologie, Göttingen Studien 2 (1848), 811-875; separately published: Vandenhoeck und Ruprecht, Göttingen, 1848.

[L03]

C. Livingston, A survey of classical knot concordance, preprint, arXiv:math.GT/0307077, 2003.

[M91]

J.C. Maxwell, A Treatise on Electricity and Magnetism, 3rd ed., Clarendon Press, Oxford, 1891; reprinted by Dover Publications, NY, 1954. MR 16:99b

[MT93]

W. Menasco and M.B. Thistlethwaite, The classification of alternating links, Annals of Math. 138 (1993), 113-171. MR 1230928

[M54]

J.W. Milnor, Link groups, Annals of Math. 59 (1954), 177-195. MR 17:70e

[M57]

J.W. Milnor, Isotopy of links, in Algebraic Geometry and Topology (Fox, Spencer and Tucker, eds.), Princeton Univ. Press, 1957, 280-306. MR 19:1070c

[M87]

K. Murasugi, The Jones polynomial and classical conjectures in knot theory, Topology 26 (1987), 187-194. MR 0895570

[R32]

K. Reidemeister, Knotentheorie, Springer, Berlin, 1932.

[R93]

D. Roseman, Twisting and turning in four dimensions, video made at the Geometry Center, 1993.

[S66]

N.F. Smythe, Boundary links in Topology Seminar, Wisconsin 1965 (R.H. Bing, ed.), Annals of Math. Study 60, Princeton Univ. Press, Princeton, 1966, 69-72. MR 0202100

[S77]

N. Stoltzfus, Unraveling the integral knot concordance group, Memoirs of the Amer. Math. Soc. 192, Amer. Math. Soc., Providence, RI, 1977. MR 0467764

[T76]

P.G. Tait, Recent Advances in Physical Sciences, 2nd ed., Macmillan and Co., London, 1876, 294.

[T77]

P.G. Tait, On knots, Trans. of the RSE 28 (1877), 145-190; reprinted in: P.G. Tait, Collected Scientific Papers, Vol. I, Cambridge Univ. Press, Cambridge, 1898, 273-317.

[T84]

P.G. Tait, On knots. Part II, Trans. RSE 32 (1884-1885), 327-339; reprinted in: P.G. Tait, Collected Scientific Papers, Vol. II, Cambridge Univ. Press, Cambridge, 1898, 318-333.

[T84]

P.G. Tait, On knots. Part III, Trans. RSE 32 (1884-1885), 493-506; reprinted in: P.G. Tait, Collected Scientific Papers, Vol. II, Cambridge Univ. Press, Cambridge, 1898, 335-347.

[T85]

M.B. Thistlethwaite, Knot tabulations and related results, in Aspects of Topology, LMS Lecture Series 93, Cambridge Univ. Press, Cambridge, 1985, 1-76. MR 0787823

[T87]

M.B. Thistlethwaite, A spanning tree expansion of the Jones polynomial, Topology 26 (1987), 297-309. MR 0899051

[W68]

F. Waldhausen, On irreducible -manifolds which are sufficiently large, Annals of Math. 87 (1968), 56-88. MR 0224099

[W87]

W. Whitten, Knot complements and groups, Topology 26 (1987), 41-44. MR 0880506

[W89]

E. Witten, Some geometric applications of quantum field theory, I, A.M.P. Congress, Swansea, 1988 (I. Davies, B. Simon and A. Truman, eds.), Institute of Physics, College Park, MD, 1989.

[W89]

E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), 351-399. MR 0990772