## Pacific Journal of Mathematics

### Studying links via closed braids. VI. A nonfiniteness theorem.

#### Article information

Source
Pacific J. Math., Volume 156, Number 2 (1992), 265-285.

Dates
First available in Project Euclid: 8 December 2004

https://projecteuclid.org/euclid.pjm/1102634977

Mathematical Reviews number (MathSciNet)
MR1186805

Zentralblatt MATH identifier
0780.57002

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 20F36: Braid groups; Artin groups

#### Citation

Birman, Joan S.; Menasco, William W. Studying links via closed braids. VI. A nonfiniteness theorem. Pacific J. Math. 156 (1992), no. 2, 265--285. https://projecteuclid.org/euclid.pjm/1102634977

#### References

• [Be] D. Bennequin, Entrelacements et equations de Pfaff,Asterisque, 107-108 (1983), 87-161.
• [B-M] J. Birman and W. Menasco, A Calculus on Links in S3, to appear in the Proceedings of the International Conference on Knots, Osaka, Japan, August 14-18, 1990.
• [B-M,I] J. Birman and W. Menasco,I] J. Birman and W. Menasco,I] J. Birman and W. Menasco,I] , Studying links via closed braids I: A finiteness theorem, Pacific J. Math., 154 (1992), 17-36.
• [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 IP. 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 closedbraids III: Classifying links which are closed 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 closedbraids IV: Split and composite links, Invent. Math., 102, Fasc. 1 (1990), 115-139.
• [B-M,V] J. Birman and W. Menasco,V] J. Birman and W. Menasco,V] J. Birman and W. Menasco,V] , Studying links via closed braids V: The unlink, Trans. Amer. Math. Soc, 329(1992), 585-606.
• [J] V. R. F. Jones, Hecke algebra representations of braid groups and link polynomials, Annals of Math., 126 (1987), 335-388.
• [VB] James Van Buskirk, Prime positive knots with inconjugate minimal string braid representatives,preprint, University of Oregon.

• I : Joan S. Birman, William W. Menasco. Studying links via closed braids. I. A finiteness theorem. Pacific Journal of Mathematics volume 154, issue 1, (1992), pp. 17-36.
• 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.