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Quasipositivity as an obstruction to sliceness
Author(s):
Lee
Rudolph
Journal:
Bull. Amer. Math. Soc.
29
(1993),
51-59.
MSC (1991):
Primary 57M25;
Secondary 32S55, 14H99
MathSciNet review:
1193540
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References:
- *
- D. Bennequin, Entrelacements et \'equations de Pfaff, Ast\'erisque \textbf{107--8} (1982), 87--161. MR 753131
- [1]
- A. J. Casson and C. McA. Gordon, Cobordism of classical knots, mimeographed notes (1975). MR
- [2]
- A. J. Casson and C. McA. Gordon, \emph{On slice knots in dimension three}, Amer. Math. Soc., Providence, RI, 1978 pp.~39--54. MR 520521
- [3]
- Tim D. Cochran and Robert E. Gompf, Applications of Donaldson's theorems to classical knot concordance, homology $3$-spheres and property $P$, Topology \textbf{27} (1988), 495--512. MR 976591
- [4]
- David Eisenbud and Walter Neumann, \nofrills Three-dimensional link theory and invariants of plane curve singularities, Ann. of Math. Stud., vol. 110, Princeton Univ. Press, Princeton, NJ, 1985. MR 817982
- [5]
- R. H. Fox, \emph{A quick trip through knot theory} (M. K. Fort, Jr., ed.), Prentice-Hall, Englewood Cliffs, NJ, 1962 pp.~120--167. MR 140099
- [6]
- R. H. Fox and J. W. Milnor, Singularities of $2$-spheres in $4$-space and cobordism of knots, Osaka J. Math. \textbf{3} (1966), 257--267. MR 211392
- [7]
- J. Franks and R. F. Williams, Braids and the Jones-Conway polynomial, Trans. Amer. Math. Soc. \textbf{303} (1987), 97--108. MR 896009
- [8]
- Michael Freedman, A surgery sequence in dimension $4;$ the relations with knot concordance, Invent. Math. \textbf{68} (1982), 195--226. MR 666159
- [9]
- Rob Kirby, \emph{Problems in low dimensional manifold theory}, Amer. Math. Soc., Providence, RI, 1978 pp.~273--312. MR 520548
- [10]
- P. Kronheimer and T. Mrowka, Gauge theory for embedded surfaces. {\rm I}, preprint, 1991. MR 1241873
- [11]
- L\^e D\~ung Tr\'ang, Sur les n{\oe }uds alg\'ebriques, Compositio Math. \textbf{25} (1972), 281--321. MR 320000
- [12]
- Ronnie Lee and Dariusz M. Wilczy\'nski, preprint, 1992. MR 1161289
- [13]
- J. Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. \textbf{44} (1969), 229--244. MR 246314
- [14]
- J. W. Milnor, \emph{Infinite cyclic coverings}, Prindle, Weber, and Schmidt, Boston, MA, 1968 pp.~115--133. MR 242163
- [15]
- J. W. Milnor, \nofrills Singular points of complex hypersurfaces , Ann. of Math. Stud., vol. 61, Princeton Univ. Press, Princeton, NJ, 1968. MR 239612
- [16]
- H. R. Morton, Seifert circles and knot polynomials, Math. Proc. Cambridge Philos. Soc. \textbf{99} (1986), 107--110. MR 809504
- [17]
- W. D. Neumann, Complex algebraic plane curves via their links at infinity, Invent. Math. \textbf{198} (1989), 445--489. MR 1022302
- [18]
- Lee Rudolph, A characterization of quasipositive Seifert surfaces \RM (Constructions of quasipositive knots and links. {\rm III)}, Topology \textbf{31} (1992), 231--237. MR 1167166
- [19]
- Lee Rudolph, Algebraic functions and closed braids, Topology \textbf{22} (1983), 191--201. MR 683760
- [20]
- Lee Rudolph, Braided surfaces and Seifert ribbons for closed braids, Comment. Math. Helv. \textbf{58} (1983), 1--37. MR 699004
- [21]
- Lee Rudolph, \emph{Constructions of quasipositive knots and links. {\rm I}}, Kundig, Geneva, 1983 pp.~99--122. MR 728589
- [22]
- Lee Rudolph, \emph{Constructions of quasipositive knots and links. {\rm II}}, Amer. Math. Soc., Providence, RI, 1984 pp.~485--491. MR 780596
- [23]
- Lee Rudolph, Embeddings of the line in the plane, J. Reine Angew. Math. \textbf{337} (1982), 113--118. MR 676044
- [24]
- Lee Rudolph, Quasipositive annuli \RM (Constructions of quasipositive knots and links. \rm IV), J. Knot Theory Ramif. \textbf{1} (1993), 451--466. MR 1194997
- [25]
- Lee Rudolph, Quasipositive plumbing \RM (Constructions of quasipositive knots and links. \rm V), preprint. MR 1452826
- [26]
- Lee Rudolph, Quasipositivity and new knot invariants, Rev. Mat. Univ. Complutense Madrid \textbf{2} (1989), 85--109. MR 1012106
- [27]
- Lee Rudolph, Some topologically locally-flat surfaces in the complex projective plane, Comment. Math. Helv. \textbf{59} (1984), 592--599. MR 780078
- [28]
- Lee Rudolph, Special positions for surfaces bounded by closed braids, Rev. Mat. Iberoamericana \textbf{1} (1985), 93--133. MR 836285
- [29]
- Lee Rudolph, \emph{Totally tangential links of intersection of complex plane curves with round spheres}, de~Gruyter, Berlin, 1992 pp.~343--349. MR 1184419
- [30]
- A. G. Tristram, Some cobordism invariants for links, Math. Proc. Cambridge Philos. Soc. \textbf{66} (1969), 251--264. MR 248854
- [31]
- O. Ja. Viro, Branched coverings of manifolds with boundary, and invariants of links. \rm I, Math. USSR-Izv. \textbf{7} (1973), 1239--1256. (Russian) MR 370605
- [32]
- B. Yu, A note on an invariant of Fintushel and Stern, Topology Appl. \textbf{38} (1991), 137--145. MR 1094546
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Additional Information:
DOI:
10.1090/S0273-0979-1993-00397-5
PII:
S 0273-0979(1993)00397-5
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