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Celebratio Mathematica

Joan S. Birman

Correspondence with Vaughan Jones

Editor’s Note

We are pleased to pub­lish in Cel­eb­ra­tio for the first time holo­graph let­ters from Vaughan Jones to Joan Birman. The bulk of these were sent over a peri­od from 1984 to mid-1990s. A few of the let­ters are un­dated. Such let­ters re­mind us that the speed and abund­ance of email can ob­scure one kind of ex­per­i­ence: the chance to see how ideas writ­ten out by hand on pa­per em­body a thought pro­cess, not merely a res­ult.

Among these let­ters is one [6] (dated 31 May 1984, from Metuchen, New Jer­sey) in which Jones de­scribes a “new knot in­vari­ant” — what we now know as the Jones poly­no­mi­al.

Letters

[1] V. Jones: Notes for J. Birman, un­dated. About the right way to write the rep­res­ent­a­tion of \( B_6 \). misc

[2] V. Jones: Notes for J. Birman, un­dated. About rep­res­ent­a­tions of map­ping class groups. misc

[3] V. Jones: Notes for J. Birman, un­dated. About nor­mal­iz­a­tion for 3-braids. misc

[4] V. Jones: Let­ter to J. Birman of 14 Novem­ber 1984. About bridge/plait “thing”. misc

[5] V. Jones: Let­ter to J. Birman of 21 Novem­ber 1984. About cal­cu­lat­ing the trace poly­no­mi­al in one vari­able for a 6-plat. misc

[6] V. Jones: Let­ter to J. Birman of 31 May 1984. About the de­tails of his new knot in­vari­ant. misc

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

[8] V. Jones: Let­ter to J. Birman of 15 May 1985. Ob­ser­va­tion that the one-vari­able poly­no­mi­al sat­is­fies a skein re­la­tion. misc

[9] V. Jones: Let­ter to J. Birman of 31 Janu­ary 1986. About new draft of his pa­per. misc

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

[11] V. Jones: Let­ter to J. Birman, un­dated, c.1990. About matrices in \( \mathrm{SL}(5,\mathbb{R}) \). misc

[12] V. Jones: Email to J. Birman of 12 June 1990. About braid­ings. misc