Some References for Knots and Braids (Math 661), Fall 2003
Disclaimer: This is not intended to be anywhere near a complete list of the many good references on knots and braids. Also, the list will almost certainly grow and change as the semester progresses.
Texts
Algebraic Topology
- Allen Hatcher, Algebraic Topology , Cambridge University Press (2002).
- W. S. Massey, Algebraic Topology: An Introduction, Springer-Verlag (1967).
Knot Theory, Braid Groups
- Colin Adams, The Knot Book, Freeman (1994).
- Joan Birman, Braids, Links and Mapping Class Groups, Princeton University Press (1974).
- Gerhard Burde and Heiner Zieschang, Knots, De Gruyter (2003).
- W. B. Raymond Lickorish, An Introduction to Knot Theory, Springer-Verlag (1997).
- Charles Livingston, Knot Theory, MAA Monographs #24 (1993).
- L. P. Neuwirth, Knot Groups, Princeton University Press (1965).
- V. V. Prasolov and A. B. Sossinksy, Knots, Links, Braids and 3-Manifolds, Trans. of Mathematical Monographs v. 154, AMS (1997).
- Dale Rolfsen, Knots and Links, Publish or Perish, Inc. (1990).
Combinatorial Group Theory
- Roger C. Lyndon and Paul E. Schupp, Combinatorial Group Theory, Springer (1977).
- Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial Group Theory, Interscience Publishers (1966).
Papers
- Stephen Bigelow. Braid groups are linear, J. AMS, 14 (2) 2001, 471--486.
- Stephen Bigelow The Burau representation of the braid group $B_n$ is not faithful for $n = 5$, Geometry and Topology {\bf 3} (1999), 397-404.
- Joan S. Birman and Elizabeth Finkelstein,
Studying surfaces via closed braids, J. Knot Theory and Its Ramifications, 7 (3) 1998, 267--334.
- Joan S. Birman and Michael D. Hirsch,
A new algorithm for recognizing the unknot, GT 2 1998, 175--220.
- Joan Birman, Ki Hyoung Ko, and Sang Jin Lee,
A new approach to the word and conjugacy problems in the braid groups
, Adv. in Math. 139 1998, 322--353.
- Joan Birman, Ki Hyoung Ko, and Sang Jin Lee,
The infimum, supremum, and geodesic length of a braid conjugacy class, Adv. in Math. 164 2001, 41--56.
- Joan Birman and William Menasco, Studying links via closed braids V : the unlink, Trans. AMS, 329 (2) 1992, 585 -- 606.
- Joan Birman, Marta Rampichini, Paolo Boldi, and Sebastiano Vigna, Towards an Implementation of the B-H algorithm for recognizing the unknot, J. Knot Theory and Its Ramifications, 11 (4) 2002, 601--645.
- Ryan Budney, On the image of the Lawrence-Krammer representation 2002, arXiv:math.GT/0202246.
- Nuno Franco and Juan Gonzalez-Meneses, Conjugacy problem for braid groups and Garside groups, J. Alg., 266 2003, 112--132.
- Knots, Braids, and Mapping Class Groups -- Papers Dedicated to Joan S. Birman, ed. Jane Gilman, William W. Menasco, and Xiao-Song Lin, 2001.
- V. F. R. Jones, Hecke algebra representations of braid groups and link polynomials , Annals of Math., 126 1987, 335--388.
- Dann Krammer. The braid group $B_4$ is linear, Invent. Math., 142 (3) 2000, 451--486.
- Ivan Marin. On the representation theory of braid groups
, preprint, 2003.
- H. R. Morton. Threading knot diagrams, Math. Proc. Camb. Phil. Soc., 99 1986, 247--260.
- V. Turaev. Faithful Linear Representations of the Braid Groups
, 2000, arXiv:math.GT/0006202.
- Pierre Vogel. Representation of links by braids: A new algorithm, Comment. Math. Helvetici, 65 (1) 1990, 104--113.
- Gretchen Wright. A foliated disk whose boundary is Morton's irreducible 4-braid, Math. Proc. Camb. Phil. Soc., 128 2000, 95--101.
- Shuji Yamada. The minimal number of Seifert circles equals the braid index of a link, Invent. Math., 89 (2) 1987, 347--356.