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.
