Arc presentations of knots and links

Peter Cromwell

Banach Center Publications (1998)

  • Volume: 42, Issue: 1, page 57-64
  • ISSN: 0137-6934

Abstract

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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].

How to cite

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Cromwell, Peter. "Arc presentations of knots and links." Banach Center Publications 42.1 (1998): 57-64. <http://eudml.org/doc/208825>.

@article{Cromwell1998,
abstract = {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].},
author = {Cromwell, Peter},
journal = {Banach Center Publications},
keywords = {arc presentation; arc index},
language = {eng},
number = {1},
pages = {57-64},
title = {Arc presentations of knots and links},
url = {http://eudml.org/doc/208825},
volume = {42},
year = {1998},
}

TY - JOUR
AU - Cromwell, Peter
TI - Arc presentations of knots and links
JO - Banach Center Publications
PY - 1998
VL - 42
IS - 1
SP - 57
EP - 64
AB - 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].
LA - eng
KW - arc presentation; arc index
UR - http://eudml.org/doc/208825
ER -

References

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  1. [B-M] J. S. Birman and W. W. Menasco, Special positions for essential tori in link complements, Topology 33 (1994) 525-556. Zbl0833.57004
  2. [Br] H. Brunn, Über verknotete Kurven, Verhandlungen des ersten Internationalen Mathematiker-Kongresses (Zürich, 1897), Leipzig, 1898. 
  3. [Cr] P. R. Cromwell, Embedding knots and links in an open book I: Basic properties, Topology and its Applications 64 (1995), 37-58. Zbl0845.57004
  4. [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. Zbl0860.57007
  5. [Li] W. B. R. Lickorish, Linear skein theory and link polynomials, Topology and its Applications 27 (1987), 265-274. Zbl0638.57005
  6. [Nu1] I. J. Nutt, Braid index of satellite links, Ph.D. thesis, University of Liverpool. 1995. 
  7. [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) 
  8. [Nu3] I. J. Nutt, Arc index and the Kauffman polynomial, J. Knot theory and its Ramifications 6 (1997), 61-77. Zbl0879.57009
  9. [Ro] D. Rolfsen, Knots and links, Publish or Perish Inc. (1976) 
  10. [Th1] M. B. Thistlethwaite, Kauffman's polynomial and alternating links, Topology 27 (1988), 311-318. Zbl0667.57002
  11. [Th2] M. B. Thistlethwaite, On the Kauffman polynomial of an adequate link, Invent. Math. 93 (1988), 285-296. Zbl0645.57007

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