Celebratio Mathematica

Michael H. Freedman


The cru­cial, and last, step in the proof of the to­po­lo­gic­al 4-di­men­sion­al Poin­caré Con­jec­ture is a del­ic­ate and sur­pris­ing de­com­pos­i­tion-space ar­gu­ment. Here are Mike’s hand­writ­ten notes [1] show­ing that the de­com­pos­i­tion \( \mathcal{D} \) is shrink­able. In his work up to this step, Mike had “ex­plored” a Cas­son handle by em­bed­ding “towers,” rather like a room full of cob­webs whose com­ple­ments are count­ably many re­gions; then, he col­lapses these re­gions to points. Un­be­liev­ably, this works!

Also, three un­pub­lished non-math­em­at­ic­al works of Mike’s, one [3] (men­tioned in his bio) from work for JASON, and two non-math­em­at­ic­al vign­ettes [2], [4] from his youth.

Fi­nally, a hard to ob­tain work [5] that is a pre­curs­or to the proofs of Marden’s con­jec­ture by Agol and by Calegari and Gabai.


[1]M. H. Freed­man: [Un­pub­lished hand­writ­ten notes].

[2]M. H. Freed­man: Jon Loni’s Stoney Point mas­sacre: A story twice re­told, 1986.

[3]M. H. Freed­man: A pro­pos­al on Panama, 1988.

[4]M. H. Freed­man: Night climb­ing, 1990.

[5]M. H. Freed­man and V. S. Krushkal: “Notes on ends of hy­per­bol­ic 3-man­i­folds” in Thir­teenth an­nu­al work­shop in geo­met­ric to­po­logy (Col­or­ado Springs, CO, June 13–15, 1996). The Col­or­ado Col­lege, 1997. In­form­al pub­lic­a­tion of The Col­or­ado Col­lege, 1997.