Celebratio Mathematica

James M. Kister

Remembrances of Jim Kister

by Robert Edwards

I ar­rived at the Uni­versity of Michigan as a first-year math gradu­ate stu­dent in 1965, with a vague idea that I wanted to ex­plore the field of to­po­logy. Which as­pects I wasn’t sure, but as an un­der­gradu­ate I was en­thused by the ma­ter­i­al in the re­cently pub­lished to­po­logy book by Hock­ing and Young. I was happy to dis­cov­er that the to­po­logy fac­ulty at U Mich had a broad span, of­fer­ing stu­dents many op­tions. Be­fore long I was cap­tiv­ated by the nuts-and-bolts sub­ject mat­ter of so-called geo­met­ric to­po­logy, most vividly con­veyed by Jim Kister’s lec­tures and in­sights. He had a knack for present­ing the­or­ems and proofs, and de­scrib­ing the rel­ev­ant spaces and con­struc­tions, with just the right level of de­tail. Ques­tions were al­ways wel­comed and answered without any in­dic­a­tion that he con­sidered them na­ive, as of­ten they were. When he got stuck, or wound up a wrong al­ley, he freely con­fessed his mis­step, of­ten shar­ing his think­ing in a man­ner that was more en­light­en­ing than the proof he was stum­bling through. Jim was re­garded as a sort of loc­al to­po­lo­gic­al hero for his pa­per show­ing that to­po­lo­gic­al mi­crobundles con­tained, and so were equi­val­ent to, genu­ine \( \mathbb{R}^n \) bundles, a res­ult that im­me­di­ately rendered ob­sol­ete Mil­nor’s elab­or­ate, some­what kludgey the­ory of mi­crobundles.

By the end of my second year I had de­term­ined that Jim was my pre­ferred choice for thes­is ad­visor. I planned to ap­proach him at the start of the next fall term, but un­for­tu­nately I learned then that he had just be­gun a year­long leave at UCLA. Oh well. So I post­poned choos­ing an ad­visor, put­ting my third year to good use plow­ing through Hurewicz and Wall­man’s book Di­men­sion The­ory, Mil­nor’s notes on dif­fer­en­tial to­po­logy, and a num­ber of oth­er valu­able books and pa­pers.

At the start of my fourth fall term Kister had re­turned, and so I screwed up my cour­age to ask him if I could work with him. He replied that he had heard that I did very well in a read­ing course the pre­vi­ous year with Pro­fess­or X, and that he had hopes that I might be­come that pro­fess­or’s first Ph.D. stu­dent. No way, I thought to my­self, re­call­ing that un­pleas­ant ex­per­i­ence. After hem­ming and haw­ing a bit, Jim fetched a pre­print from his gi­ant stack, say­ing that this pa­per made some bold claims which he was skep­tic­al of, but that he didn’t have the time to dig in­to it. Maybe I could?

Chal­lenge ac­cep­ted. It turned out to be easy. I quickly dis­covered that the na­ive gradu­ate stu­dent au­thor had made an in­ex­cus­able gaffe.1 I was eu­phor­ic when Jim was clearly pleased with my re­port.

Then once again he reached in­to his tower­ing pile and handed me an­oth­er pre­print, this one from the noted Rus­si­an to­po­lo­gist Černavskiĭ, who was claim­ing to prove the loc­al con­tract­ib­il­ity of the homeo­morph­ism group of a man­i­fold. This was big! Same re­quest from Jim. This one took a few days, but I found a flaw in the ar­gu­ment, which I ex­plained to Jim.2 Again Jim seemed de­lighted with my work, and so he pulled yet an­oth­er pre­print from his pile, say­ing that this one looked like a win­ner.

It was Rob Kirby’s ini­tial pre­print on his break­through tri­an­gu­la­tion work us­ing the tor­us trick, and it in­cluded the loc­al con­tract­ib­il­ity of the homeo­morph­ism group of a man­i­fold al­most as an af­ter­thought.3 The math­em­at­ics in that pre­print re­lied heav­ily on the homeo­morph­ism push-pull tech­nique that Kister had mastered and I had come to rel­ish. I re­por­ted back to Jim a few days later, say­ing that an easy co­rol­lary of Kirby’s work was that the Cov­er­ing Iso­topy The­or­em (well-known and power­ful in the smooth and PL world) now held in the world of homeo­morph­isms of to­po­lo­gic­al man­i­folds. He was de­lighted (say­ing that he sus­pec­ted that co­rol­lary him­self). What happened next astoun­ded me (and still does).

Jim pondered a bit, then picked up the phone and dialed. (Re­col­lect­ing loosely here: “Rob, I have a stu­dent here who has read your pre­print, and he says that the to­po­lo­gic­al Cov­er­ing Iso­topy The­or­em im­me­di­ately fol­lows (with all of its at­tend­ant con­sequences).4 This ought to be writ­ten up, to make sure it’s right. Would it be okay if my stu­dent did so?” Kirby’s as­sent was (need­less to say) a ma­jor mo­ment in my math­em­at­ic­al ca­reer. I still can’t be­lieve that Jim just picked up the phone and called Kirby.

One more gradu­ate ca­reer story, which ex­hib­its Jim’s sense of open­ness and fair­ness. Thes­is now in hand (thanks, Rob), the top­ic of my first job came to the fore. After ap­plic­a­tions were mailed and sup­port­ing let­ters writ­ten, one day Jim men­tioned to me al­most in passing, “This year I am blessed to have two ex­cel­lent gradu­at­ing Ph.D. stu­dents. Since both of you have pro­duced su­perb theses, I couldn’t dif­fer­en­ti­ate in any way my re­com­mend­a­tions for the two of you. So I wrote identic­al let­ters.” He then flashed them to me quickly to show his point, and then read a few key sen­tences. I was em­bar­rassed and de­lighted. Es­pe­cially when we both re­ceived very at­tract­ive identic­al of­fers from Cor­nell. The only reas­on I didn’t ac­cept was that I was offered an ONR postdoc at Prin­ceton, which was too tempt­ing to pass up.

At Prin­ceton and after, my in-per­son con­tact with Jim was in­fre­quent, al­though the sup­port he gave and let­ters he wrote for me in sub­sequent years seemed to have worked, for which I was (and re­main) most grate­ful. I will forever re­mem­ber Jim for his won­der­ful math­em­at­ics, and more im­port­ant (for me) his wise guid­ance and kind coun­sel.