#### by Martin Scharlemann

I was Rob Kirby’s third Ph.D. student, and his first student at Berkeley. Rob was my fourth prospective Ph.D. advisor there, and the only one to really help. Here is the story.

In 1969 I entered the UC Berkeley Ph.D. program, primarily attracted by Berkeley’s excellent reputation in topology. I was not alone: aspiring topology students were pouring into UCB, many hoping to work with such topological luminaries as Stephen Smale, Ed Spanier, or John Stallings (and that’s just the S’s). Next to Princeton, UC Berkeley was the world’s center of cutting-edge topology. Beyond its stellar regular faculty, it also attracted young hot-shot summer visitors like the charismatic Dennis Sullivan.

But when I arrived at Berkeley, I soon found that there were
negatives. The physical setting for the Math Department was grim.
Evans Hall was not yet completed and the Mathematics Department was
crammed into a small building, one we shared with astronomers. I was
assigned a desk in a large windowless office with about ten other
graduate students. (A particularly messy desk belonged to a guy named
Bill Thurston.)
The library was small and hard to use, but I suppose
it worked OK for the truly focused. Seeing one student check out maybe
half a dozen issues of *The Journal of Differential Geometry*,
while returning a like number, I thought, “Who is that guy?” (Answer:
Shing-Tung Yau.)

There was, famously, political turmoil in the streets. This was both exciting and scary, but always inconvenient. My first Halloween evening I was blocked from going home by the Oakland Tactical Squad (aka The Blue Meanies), who were clearing Telegraph Avenue of rioters. My first naïve reaction: “Where did those guys get such great Halloween costumes!?” Classes were canceled for much of the year because of militants’ threats. And always, always the military draft and the Vietnam War hung like raptors overhead, waiting for students to stumble.

As I worked toward passing quals, a further worry nagged: it was going to be really hard to find a dissertation supervisor, especially in topology. There were lots of eager students, while many of the famous faculty topologists had moved on to other subjects. (Stephen Smale, for one example, was doing economics.) And so it was that by my third year I had approached three different faculty members; none would help with my dissertation.

At that point Rob Kirby arrived, hired away from UCLA after his foundational work on the triangulation of manifolds. His first day on campus, I camped outside his office, waiting for him to have a free moment. When he did, I introduced myself and immediately asked him if he would supervise my dissertation. He was of course surprised, but said something that I took to be positive like, “I’ll suggest some things to read.” And so we began. I was delighted at how willing he was to take me on. Or so I hoped, since I couldn’t really be sure that he had in fact agreed.

What Rob encouraged me to read was Browder’s new book [e1] on simply-connected high-dimensional surgery, and the few papers that then existed on 4-manifolds. (This was a time, before Donaldson, Freedman, and the Kirby calculus, when one could learn all that was known about 4-manifolds in a matter of weeks.) Browder’s account of surgery was beautiful mathematics, and Rob mostly let me learn it on my own. We’d meet in an ad hoc way — when I had something to talk about I’d drop by; otherwise I’d just keep reading. He had no teaching duties during his early months at Berkeley, and also had no other students to work with — a lucky time for me. With his first (advanced graduate) class, I finally met my future comrades: There were perhaps 40 students in the classroom when Rob walked in to begin his Berkeley teaching. He looked stunned at the number, and his first act was to write the name of the class on the board, expecting there was a mistake and that many would leave. When nobody did, he laughed and said, “I hope you’re not all looking for a thesis advisor!”

Quite a few of the students were, and soon Rob had perhaps 10 advisees. He thus began a dramatic change in the culture of UCB topology. Instead of trying to avoid potential students, as many overwhelmed faculty did, Rob welcomed them, eventually organizing a seminar in which students mostly talked to each other. Not all prospered from his laissez-faire approach, but many did, as a list of his early students shows. Eventually added to the mix were Rob’s coauthor Larry Siebenmann and also Siebenmann’s French students. They would come in the summers, offering seminars of such length that occasionally most of the Anglophones would leave, and the language would switch to French.

Sometime in all of this I started writing papers: first with Rob and then with Larry Siebenmann. My first paper with Rob was based on a hope of his for a new topological category called MCCG [1]. Details aren’t important: it didn’t work out and my contribution was mostly to show that it couldn’t. Our following paper on the Poincare homology sphere [2] fit perfectly into my dissertation research, and is the only paper I have written that earned royalties, via a Soviet translation. Not sure Rob ever got his share.

The papers with Siebenmann [e2], [e3] came about because he and I (unbeknownst to each other) were trying to understand smooth homeomorphisms: homeomorphisms between smooth manifolds which were only smooth maps in one direction. I had amateurish first results; Larry was developing an entire theory. When Rob learned of our mutual interest, he thoughtfully suggested to Larry that he take me on as an apprentice, and Larry was kind enough to do so. That’s how I learned Larry’s very effective pre-computer method of writing papers: a few sentences hand-written on each page, pages piled in massive stacks, then easily reshuffled as the argument emerged.

By the time I was ready to finish at Berkeley, I’d already written a few papers on my own. In part this was a consequence of Rob’s excellent advice to stay on a fifth year instead of finishing in four, since institutions typically start the publication clock with the Ph.D. With several papers to choose from, I asked Rob my final year what I should do about my dissertation: staple the papers together, or just choose one. Rob’s memorable advice: “Hmm, I guess I should read it. Why don’t you pick whatever’s shortest?” So I did.

Berkeley had no requirement for a thesis defense, so that seemed to be the end of it. Rob thought it might be a good idea, though, for me to talk about the results in his seminar. Of course I agreed, expecting an audience of students, most of them Rob’s or intending to be Rob’s. But when I walked in, there were students, sure, but also — the luminaries! Rob had arranged, on the down-low, an ad hoc thesis defense, by encouraging the senior topology faculty to attend my talk. This was a shock, but not a bad one; I could thereafter add to my mental résumé that I once gave a seminar talk with Ed Spanier in the audience. The faculty presence was also mathematically useful: Jack Wagoner spotted a gap in my argument, but fortunately one that I was able to fill in real time at the board, a fix I later incorporated into my dissertation [e4].

There are so many other stories from Berkeley at that time: can I mention that I lived just half a block from the original Peet’s, where buzzy coffee refills cost just 25¢? That the rent on our three-bedroom Walnut Street cottage was \$125/month? That a small French restaurant named Chez Panisse opened around the corner, but surely couldn’t last long — who in Berkeley would pay \$6 dollars for dinner? That my future wife’s apartment shared a wall with what would become a Symbionese Liberation Army arms dump? I’ll forgo these stories, wanting to focus here on how Rob Kirby made such a difference both to the environment of the Berkeley Mathematics Department and to my personal mathematical development. But if you are curious, and see me at a conference, don’t be shy about asking for more!

*Martin Scharlemann received his Ph.D. in mathematics from UC Berkeley in 1974. Following a year at the Institute for Advanced Studies and a year at the University of Georgia, he moved to UC Santa Barbara, where he is now a Distinguished Professor Emeritus.*