Celebratio Mathematica

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.