Links in an open book decomposition and in the standard contact structure

Proceedings of the American Mathematical Society

Volumn 134, Issue 12, 2006, Pages 3697-3702

  Matsuda, Hiroshi ^a,b  

^a HIROSHIMA UNIVERSITY   (Japan)

^b Howard Hughes Medical Institute   (United States)

Author keywords

Arc presentation; Legendrian knot

Indexed keywords

EID: 33845644183     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-06-08400-0     Document Type: Article

References (12)

1. D. Bennequin, Entrelacement et équaations de Pfaff, Astérisque 107-108 (1983) 87-161. MR0753131 (86e:58070)
2. J. Birman, W. Menasco, Special positions for essential tori in link complements, Topology 33 (1994) 525-556;
3. Erratum: Topology 37 (1998) 225. MR1286930 (95i:57006) MR1480888 (98j:57004)
4. J. Birman, W. Menasco, Stabilization in the braid groups II: Transversal simplicity of knots, preprint available at arXiv:math.GT/0310280.
5. J. Birman, N. Wrinkle, On transversally simple knots, J. Differential Geom. 55 (2000) 325-354. MR1847313 (2002g:57008)
6. H. Brunn, Uber verknotete Kurven, in: Verhandlungen des ersten Internationalen Mathematiker-Kongresses, Zurich, 1897 (1898) 256-259.
7. P. Cromwell, Embedding knots and links in an open book I: Basic properties, Topology Appl. 64 (1995) 37-58. MR1339757 (96g:57006)
8. I. Dynnikov, Arc-presentations of links. Monotonic simplification, preprint available at arXiv:math.GT/0208153.
9. J. Etnyre, K. Honda, Knots and contact geometry I: torus knots and the figure eight, Journal of Sympl. Geom. 1 (2001) 63-120. MR1959579 (2004d:57032)
10. N. Kuhn, A conjectual inequality on the slice genus of links, Ph.D. Thesis, Princeton University, 1984.
11. H. Lyon, Torus knots in the complements of links and surfaces, Mich. Math. J. 27 (1980) 39-46. MR0555835 (81b:57005)
12. L. Rudolph, An obstruction to sliceness via contact geometry and "classical" gauge theory, Invent. Math. 119 (1995) 155-163. MR1309974 (95k:57013)