#### by Raymond Lickorish

__\( (n-1) \)__-sphere

__\( S^{n-1} \)__in

__\( S^n \)__there was a copy of the annulus

__\( S^{n-1} \times I \)__. Kirby’s work on this not only solved one of the then outstanding problems on topological manifolds but it led, in joint work with Larry Siebenmann, to a comprehensive theory of the triangulation of topological manifolds, of dimension at least five, as piecewise-linear manifolds (there is one obstruction). Together with reprints of their original paper this is all described in their book [2]. The work on the Kirby moves had a strange effect. The actual result was not really used until the arrival of quantum invariants some dozen years later, but people’s attitudes were changed. Knowledge that anything could be done with just two moves meant that those two were the ones to play with and many did so.

Rob and I first met as visitors to the University of Wisconsin in the Fall Semester of 1967. He lectured on topological manifolds, I on piecewise-linear ones. Born six days apart, so at the same stage in life, we began a life-time’s friendship with regular correspondence. In mathematical research, personal contacts were important before the days of e-mail, the arXiv, MathSciNet, TeX, Google and Zoom. Rob returned to UCLA at Christmas 1967, preferring the mountains and rivers of California to a Wisconsin winter. Over the years we visited each other many times in Berkeley and in Cambridge. Sometimes we were accompanied by students and Rob had many of them. At the last count he has had 53 students who, he claimed, taught each other. The gatherings at these visits eventually climaxed in two three-week conferences in Cambridge in 1981 and 1984. These meetings were entirely informal. Anyone was welcome for any length of time. There was no funding (though perhaps Rob’s NSF grant helped some of his students) and no proceedings. We had two talks every afternoon followed for some, including Rob, by football on nearby Lammas Land. The Cambridge departmental facilities were made available without charge and empty student accommodation was cheap. Rob found that he rather liked Great Britain, including its weather and food. He has visited often, with Colin Rourke in Warwick and Andrew Ranicki in Edinburgh being particular friends. His British connection climaxed with his appointment in 1992 as a Rothschild Visiting Professor at the Isaac Newton Institute during the Institute’s first session, entitled Low Dimensional Topology and Quantum Field Theory. This was accompanied by a visiting fellowship at Emmanuel College.

Rob’s first marriage broke up around 1978 leaving him in charge of two young children, a large house and not much money. There was pressure on time available for mathematics. Our two families did however join in 1980 for a stay in the cabin of Jim Van Buskirk (University of Oregon) by the Metolius River in the Oregon Cascades, with swimming in the local Scout Lake.

The work that produced the Kirby moves on 3-manifolds led to a Kirby
notation for presenting handle decompositions of 4-manifolds. Over
the years Rob and several of his students explored the considerable
intricacies of
this. Berkeley became a centre for this type of
work. The culmination was Rob’s Springer Lecture Notes
book *The Topology of 4-Manifolds*
[5]
which includes
Mike Freedman’s
use of
Andrew Casson’s
handles and a short description of
some of
Simon Donaldson’s
results.

A most important part of Rob’s career has been not only *doing*
research but encouraging research by others. This was typified by his
1976 compendium entitled
*Problems in low dimensional manifold theory*
[3].
This listed 68 problems, attributed to a wide range
of authors, together with remarks on the appropriate state of
knowledge at the time. Known as the *Kirby problem list*, this set
the agenda for many years of low dimensional topology research. Many
of his graduate students went on to their own distinguished university
careers. He kept in touch with them, often by writing papers jointly
with them. Rob and I wrote just one paper together
[4];
it gave us pleasure at the time but does not seem important now! Back in
those Wisconsin days of 1967 one consulted journals in a department’s
library, or borrowed them from the library, to learn of any recent
progress of relevance to one’s research. The number of journals has
greatly increased and their purpose is much changed. In more recent
years Rob has played a leading role in promoting electronic journals
and in campaigning for a fair financial deal from journal publishers
for mathematicians and their universities.

*Raymond Lickorish is Professor Emeritus of Geometric Topology
in the University of Cambridge where, for five years, he was head of
the Department of Pure Mathematics and Mathematical Statistics. He
is a Fellow of Pembroke College where, for many years he was
Director of Studies in Mathematics. He has held university visiting
positions in Wisconsin, Berkeley, Santa Barbara, Texas, Los Angeles
and Melbourne. In research he investigated twisting automorphisms of
surfaces and their interaction with surgery descriptions of
3-manifolds. He worked on piecewise-linear theory, particularly
collapsing results and unknotting theorems in high dimensions. He
was also much involved with invariant polynomials for links and
knots, after V. F. R. Jones’ initial discovery, and he has authored a
knot theory text.*