Arc presentations of knots and links

• Autorzy: Peter R. Cromwell
• Języki publikacji: EN

Abstrakty

EN

s paper presents some examples and a survey of results concerning a new way of presenting knots and links, together with the corresponding link invariant. More detailed accounts are given in [Cr, C-N, Nu1, Nu2, Nu3].

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1998
• Tom: 42
• Numer: 1
• Strony: 57-64

Daty

wydano

1998

Twórcy

autor

Peter R. Cromwell

• Department of Pure Mathematics, University of Liverpool, PO Box 147, Liverpool, L69 3BX, England

Bibliografia

• [B-M] J. S. Birman and W. W. Menasco, Special positions for essential tori in link complements, Topology 33 (1994) 525-556.
• [Br] H. Brunn, Über verknotete Kurven, Verhandlungen des ersten Internationalen Mathematiker-Kongresses (Zürich, 1897), Leipzig, 1898.
• [Cr] P. R. Cromwell, Embedding knots and links in an open book I: Basic properties, Topology and its Applications 64 (1995), 37-58.
• [C-N] P. R. Cromwell and I. J. Nutt, Embedding knots and links in an open book II: Bounds on arc index, Math. Proc. Cambridge Philos. Soc. 119 (1996), 309-319.
• [Li] W. B. R. Lickorish, Linear skein theory and link polynomials, Topology and its Applications 27 (1987), 265-274.
• [Nu1] I. J. Nutt, Braid index of satellite links, Ph.D. thesis, University of Liverpool. 1995.
• [Nu2] I. J. Nutt, Embedding knots and links in an open book III: On the braid index of satellite links, Preprint 1995. (University of Liverpool)
• [Nu3] I. J. Nutt, Arc index and the Kauffman polynomial, J. Knot theory and its Ramifications 6 (1997), 61-77.
• [Ro] D. Rolfsen, Knots and links, Publish or Perish Inc. (1976)
• [Th1] M. B. Thistlethwaite, Kauffman's polynomial and alternating links, Topology 27 (1988), 311-318.
• [Th2] M. B. Thistlethwaite, On the Kauffman polynomial of an adequate link, Invent. Math. 93 (1988), 285-296.