Pacific Journal of Mathematics

Studying links via closed braids. I. A finiteness theorem.

Joan S. Birman and William W. Menasco

Article information

Source
Pacific J. Math., Volume 154, Number 1 (1992), 17-36.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102635729

Mathematical Reviews number (MathSciNet)
MR1154731

Zentralblatt MATH identifier
0759.57003

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Citation

Birman, Joan S.; Menasco, William W. Studying links via closed braids. I. A finiteness theorem. Pacific J. Math. 154 (1992), no. 1, 17--36. https://projecteuclid.org/euclid.pjm/1102635729


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References

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  • [Bi] Joan S. Birman, Braids, links and mapping classgroups,Annals of Math. Studies #82, Princeton University Press, 1974.
  • [B-M] J. Birman and W. Menasco, A calculus for links in the ^-sphere, Proc. of 1990 Osaka Conference on "Knots", to appear.
  • [B-M,II] J. Birman and W. Menasco,II] J. Birman and W. Menasco,II] J. Birman and W. Menasco,II] , Studying links via closed braids II: On a theorem of Bennequin, Topology Appl., 40 (1991), 71-82.
  • [B-M,III] J. Birman and W. Menasco,III] J. Birman and W. Menasco,III] J. Birman and W. Menasco,III] , Studying links via closedbraidsIII: Classifying links whichareclosed 3'braids, Pacific J. Math., to appear.
  • [B-M,IV] J. Birman and W. Menasco,IV] J. Birman and W. Menasco,IV] J. Birman and W. Menasco,IV] , Studying links via closedbraidsIV: Split and compositelinks, Invent. Math., 102 (1990), 115-139.
  • [B-M,V] J. Birman and W. Menasco,V] J. Birman and W. Menasco,V] J. Birman and W. Menasco,V] J.Birman andW. Menasco, StudyinglinksviaclosedbraidsV: The unlink, Trans. Amer. Math. Soc,329 (1992), 585-606.
  • [B-M,VI] J. Birman and W. Menasco,VI] J. Birman and W. Menasco,VI] J. Birman and W. Menasco,VI] , Studying links viaclosedbraidsVI:A non-finiteness theorem, Pacific J. Math., to appear.
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  • [Mo1] H.Morton, Infinitelymanyfibered knots with thesame Alexanderpolyno- mial, Topology, 17 (1978), 101-104.
  • [Mo2] H.Morton, Closed braids whicharenotprime knots, Math. Proc. Camb. Phil. Soc, 86 (1979), 421-426.
  • [Mo3] H.Morton, Exchangeable braids, London Math. Soc. Lecture notes 95,Low dimensional topology ed. Fenn, 86-105.
  • [R] L.Rudolph, Specialpositionsfor surfacesboundedby closed braids, Rev. Mat. Iberoamericana, 1 no. 3 (1985), 93-133.
  • [Ta] P. G. Tait, OnKnots, in Collected Scientific Papers of P. G. Tait, Camb. Univ. Press, London, 1898,273-347.
  • [Th] W. Thurston, Onthegeometry anddynamics ofdiffeomorphismsof sur- faces, Bull. Amer. Math. Soc. (New Series) 19, No. 2 (October 1988), 417-432.

See also

  • Joan S. Birman, William W. Menasco. Studying links via closed braids. {II}. On a theorem of Bennequin. II [MR 92g:57009] Topology Appl. 40 1991 1 71--82.
  • III : Joan S. Birman, William W. Menasco. Studying links via closed braids. III. Classifying links which are closed $3$-braids. Pacific Journal of Mathematics volume 161, issue 1, (1993), pp. 25-113.
  • Joan S. Birman, William W. Menasco. Studying links via closed braids. {IV}. Composite links and split links. IV [MR 92g:57010a] Invent. Math. 102 1990 1 115--139.
  • Joan S. Birman, William W. Menasco. Studying links via closed braids. V. The unlink. V [MR 92g:57010b] Trans. Amer. Math. Soc. 329 1992 2 585--606.
  • VI : Joan S. Birman, William W. Menasco. Studying links via closed braids. VI. A nonfiniteness theorem. Pacific Journal of Mathematics volume 156, issue 2, (1992), pp. 265-285.