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Celebratio Mathematica

Joan S. Birman

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Correspondence with Dennis Johnson

Preface

by Joan Birman

The fol­low­ing eight let­ters were writ­ten by Den­nis John­son to me dur­ing the peri­od of time when he was work­ing on his found­a­tion­al pa­pers about map­ping class groups of sur­faces (see [e1], [e4], [e3], [e2], [e5], [e7], [e6], [e8] and [e9]). The let­ters evoke Den­nis as I re­mem­ber him — filled with life, en­thu­si­asm, curi­os­ity, and eager­ness to talk about math. All but one of the eight are un­dated, but the or­der in which they were writ­ten isn’t very im­port­ant. He was carving out new areas for in­vest­ig­a­tion, so new that it wasn’t even clear at the time which of the open ques­tions he was con­sid­er­ing could or would be answered. They give in­sight in­to the cre­at­ive pro­cess, in a way that is eas­ily lost in the es­sen­tial pas­sage from the let­ters to the pub­lished pa­pers.

Editor’s Note

The un­dated let­ters lis­ted here (be­low the “Ref­er­ences” sec­tion) have been pro­vi­sion­ally ordered based on in­tern­al evid­ence and on Birman’s memory of her cor­res­pond­ence with John­son. Shi­gey­uki Mor­ita’s eval­u­at­ive help in this ef­fort is greatly ap­pre­ci­ated.

Letters

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

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

[3] 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

[4] 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

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

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

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