Reminiscences of Peter Scott

We first interacted in Liverpool during 1968-69 where we discussed mostly Kirby-Siebenman work. Later we seem to have independently turned to 3-manifolds and there was some correspondence in 1972 about Waldhausen’s work as well as ‘finitely generated implies finitely presented’ for 3-manifold groups. There is some discussion of this in a survey article by Danny Wise and probably the neatest proof comes from Thomas Delzant which I described ‘Delzant’s variation of Scott Complexity’ written in Peter’s honour on his 60th birthday. Our next interactions were sporadic for a while. I remember Peter advising me that it is difficult to understand Thurston and that I should discuss with others. He then invited me to conference in 1984 that he organised with D.B.A. Epstein in Warwick. By this time he was quite well known and seemed to be determined to make a better mathematician out of me. We next met in Norman, Oklahoma in 1986, and he suggested two problems which we did together. One of them proved that certain finitely generated subgroups of distorted Kleinian groups are geometrically finite. Since then topic has been pursued by a few others. After that we met in a few conferences where we discussed how many results in 3-manifold theory may have analogues in group theory with annulus theorem as a possible candidate. But serious work on this started in 1994 when Peter visited Melbourne. During this visit Peter showed me a paper of Tukia and said that it should lead to a proof of annulus theorem for hyperbolic groups and he also suggested that I needed to read only a few pages in Tukia’s paper. It was like a thesis advisor advising a student. This was the start of an intense collaboration with Peter since then. We probably wrote over six hundred pages of mathematics together in about ten papers. We made mistakes and probably took up a wrong program. But after a lot of hard work we did achieve what we wanted and for both us it seemed the hardest work we have done. We visited each other several times and it was not always clear how the ideas originated but they seemed joint. The program was the main aim, we did not care who did the actual work. Some papers were completely Peter’s and some more or less mine though they appeared as joint papers. Sometimes there were other collaborators. For both us it was very satisfactory work with the last paper just nearing completion. ‘Beating it in to shape’ as Peter used to say. In retrospect, it seems to me that we were barking up the wrong tree though Peter did not agree with me. But along the way we did some work on intersection numbers and regular neighbourhoods which seem to be useful in other contexts too. Peter remained active until he could work no more. This last paper was written mostly by him. During this March-June, he developed another approach to regular neighbourhoods which is quite interesting and non-trivial.