Celebratio Mathematica

J. S. Birman and R. Craggs: “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

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

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

D. John­son: 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

D. John­son: 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

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

J. S. Birman and R. Craggs: “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

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

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

J. S. Birman and R. F. Wil­li­ams: “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

V. Jones: 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

V. Jones: 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

V. Jones: 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

J. S. Birman: “On the Jones poly­no­mi­al of closed 3-braids,” In­vent. Math. 81 : 2 (June 1985), pp. 287–​294. MR 799267 Zbl 0588.​57005 article

J. S. Birman and C. Series: “Geodesics with bounded in­ter­sec­tion num­ber on sur­faces are sparsely dis­trib­uted,” To­po­logy 24 : 2 (1985), pp. 217–​225. MR 793185 Zbl 0568.​57006 article

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

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

V. Jones: 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

V. Jones: 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

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

V. Jones: 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

J. S. Birman: “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

J. S. Birman and X.-S. Lin: “Knot poly­no­mi­als and Vassiliev’s in­vari­ants,” In­vent. Math. 111 : 2 (1993), pp. 225–​270. MR 1198809 Zbl 0812.​57011 article

J. S. Birman, D. John­son, and A. Put­man: “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