### An interview with Joan Birman about her mathematics

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On the __\( \mu \)__-invariant of __\( Z \)__-homology 3-spheres,”
Bull. Am. Math. Soc.
82 : 2
(March 1976),
pp. 253–255.
MR
0397734
Zbl
0343.55001
article

Letter to J. Birman, undated. About simplifications to proofs (based on phone call with Joan). misc

:Letter to J. Birman, undated. About paper identifying the kernel of one of “Joan’s” homomorphisms. misc

:
Letter to J. Birman, undated.
About paper enumerating __\( \mathbb{Z}_2 \)__ maps, proof that all the 4-intersection cases reduce, and material on intersection theory.
misc

Letter to J. Birman, undated.
About using relations in __\( \mathcal{I} \)__ to get symmetric homology spheres and new paper with description of __\( \mathcal{I}/\mathcal{C} \)__.
misc

Letter to J. Birman of 10 March 1977. Short description of machinery to be used in forthcoming paper. misc

:
The __\( \mu \)__-invariant of 3-manifolds and certain structural properties of the group of homeomorphisms of a closed, oriented 2-manifold,”
Trans. Am. Math. Soc.
237
(March 1978),
pp. 283–309.
MR
0482765
Zbl
0383.57006
article

Letter to J. Birman, undated.
About paper on torsion of maps in __\( \mathcal{I} \)__.
misc

Notes for J. Birman, undated.
About the space of Casson homomorphisms for a surface __\( K_{g,1} \)__.
misc

Knotted periodic orbits in dynamical systems, I: Lorenz’s equations,”
Topology
22 : 1
(1983),
pp. 47–82.
Part II was published in *Low-dimensional topology* (1983).
MR
682059
Zbl
0507.58038
article

Letter to J. Birman of 31 May 1984.
As a follow-up to their May 22, 1984 meeting, Jones explains to Birman, who
was not familiar with his work on type __\( \text{II}_1 \)__ factors, how that work had lead him to a formula
for a 1-variable polynomial invariant of a classical link in __\( \mathbb{R}^3 \)__. He calls his invariant __\( V (t) \)__.
Starting on page 5, he works out some of its basic elementary properties.
misc

Letter to J. Birman of 14 November 1984.
Birman and Jones had met at a conference at MSRI October 10–16, and
discussed, among other things, forming knots and links from braids, but using the connections
needed to get *plat and bridge presentations*.
misc

Letter to J. Birman of 21 November 1984. About another topic that had been discussed at the October 10–16 gathering, i.e., representations of the mapping class group of a surface of genus 2, using 6-plats. misc

:On the Jones polynomial of closed 3-braids,” Invent. Math. 81 : 2 (June 1985), pp. 287–294. MR 799267 Zbl 0588.57005 article

: “Geodesics with bounded intersection number on surfaces are sparsely distributed,” Topology 24 : 2 (1985), pp. 217–225. MR 793185 Zbl 0568.57006 article

: “Letter to J. Birman of 26 February 1985. About the formula for closed 3-braids that are knots. misc

:Letter to J. Birman, undated.
About matrices in __\( \mathrm{SL}(5,\mathbb{R}) \)__.
misc

Letter to J. Birman of 15 May 1985. About his observation that the plat representation of the 1-variable Jones polynomial satisfies a skein relation. misc

:Letter to J. Birman of 31 January 1986. A letter that told Birman about the submission of the “first draft” of “Hecke algebra representations of braid groups and link polynomials” for publication. Essentially everything that had been discussed in the letters that preceded this one (and more) appeared in the published paper. misc

:Copy of Letter to L. Kauffman of 3 October 1986. About a states model for the two-variable Jones polynomial. misc

:Email to J. Birman of 12 June 1990.
An e-mail from V Jones to J. Birman, about calculating the braid index of a
knot. To understand its content, note that near the end of Jones’
paper “Hecke algebra representations of braid groups and link
polynomials”,
there is a table
that assigns braid indices to the 84 knots from the table at the end of Rolfsen’s classic book
*Knots and Links*.
Birman had asked Jones whether he discovered new tricks for changing knots into braids,
and if not, how he had the patience to do it on so many knots? Read this 12 June 1990 e-mail
to learn his answer.
misc

New points of view in knot theory,” Bull. Am. Math. Soc. (N.S.) 28 : 2 (1993), pp. 253–287. MR 1191478 Zbl 0785.57001 article

: “Knot polynomials and Vassiliev’s invariants,” Invent. Math. 111 : 2 (1993), pp. 225–270. MR 1198809 Zbl 0812.57011 article

: “Symplectic Heegaard splittings and linked abelian groups,” pp. 135–220 in Groups of diffeomorphisms: In honor of Shigeyuki Morita on the occasion of his 60th birthday (Tokyo, 11–15 September 2006). Edited by R. C. Penner. Advanced Studies in Pure Mathematics 52. Mathematical Society of Japan (Tokyo), 2008. MR 2509710 Zbl 1170.57018 ArXiv 0712.2104 incollection

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