Celebratio Mathematica

Write something about Colin Rourke. It’s hard to say ex­actly how but I really do owe a lot of my math­em­at­ic­al de­vel­op­ment to him, and I shall al­ways be grate­ful to him for this in­flu­ence.

I ar­rived in War­wick in 1977 and at the time Colin was work­ing at the Open Uni­versity. Weekly trips to the Open Uni­versity (teach­ing via tele­vi­sion in an age be­fore the in­ter­net) in the leath­er up­holstered lux­ury of the blue Rover, one of Colin’s fa­vour­ite cars, and dis­cus­sions there were a big part of learn­ing how to talk about math­em­at­ics.

My pro­ject was to study Colin’s “pic­tures” in the con­text of group present­a­tions and try to prove the Ker­vaire con­jec­ture (adding a gen­er­at­or and a re­la­tion to a non-trivi­al group can­not make it trivi­al). This in­volved mix­ing geo­met­ric­al, to­po­lo­gic­al and al­geb­ra­ic ideas, which has al­ways been part of Colin’s main pre­oc­cu­pa­tion; later this was called geo­met­ric group the­ory. A pic­ture is ba­sic­ally a trans­vers­al­ity dia­gram, so that in­stead of think­ing of a re­la­tion in a group as a product of con­jug­ates of re­lat­ors, there is a col­lec­tion of small disks in the plane, cor­res­pond­ing to the re­lat­ors, and arcs join­ing the disks cor­res­pond­ing to the gen­er­at­ors. They are “just” dual to van Kampen dia­grams, but the to­po­lo­gic­al ori­gins are of­ten very use­ful. The con­jec­ture was proved by Kly­ach­ko [e4] for tor­sion-free groups in 1996, us­ing cars crash­ing on graphs in the 2-sphere, really not so far from the pic­tures ap­proach. Colin and Ro­ger Fenn wrote a nice ex­pos­i­tion and gen­er­al­isa­tion of this [1]. (I only man­aged a ver­sion [e2] for loc­ally in­dic­able groups, at the same time as Jim How­ie [e3] and Sergei Brod­skiĭ [e1].)

Colin didn’t do much of the one-on-one sit­ting down and dis­cuss­ing things in any sort of form­al situ­ation. One of the few oc­ca­sions when we were ac­tu­ally sit­ting at a table work­ing hard (in the kit­chen in Barby) ended when a mouse ran across the room in front of one of the cats who con­tin­ued lan­guidly clean­ing its whiskers. Colin threatened to get rid of the use­less cat who clearly wasn’t earn­ing its keep on a work­ing farm. A farm with no TV, so that when Colin made his first pro­gramme for the OU, we all went to Ian Stew­art’s house to watch it.

Soon after my ar­rival in War­wick I in­her­ited a small amount of money and bought a small ter­race house (with out­side toi­let). The re­port of the struc­tur­al solid­ity of the build­ing con­sisted of Colin go­ing up­stairs and jump­ing up and down. “It can res­ist me do­ing that so it’s ok,” he said.

Oth­er work with Colin in­volved things like bring­ing in the hay (what a happy man the day he bought his first tract­or). But in re­turn I got to drive the won­der­ful Jag­uar XK150 stored in one of the cow­sheds. And I in­her­ited the old Ray­burn stove from the kit­chen when Colin and Daphne up­graded.

There was the time Colin de­cided that his be­loved Rover had prob­lems with its cool­ing sys­tem; the usu­al acid­ic ad­dit­ives to re­move scale and rust de­pos­its had not helped. He asked at the deal­ers and they said he needed a new ra­di­at­or. He in­sisted there must be an al­tern­at­ive and fi­nally the mech­an­ic said that he sup­posed you could the­or­et­ic­ally un­weld the top and bot­tom of the ra­di­at­or and us­ing very fine wire scrape the in­sides of the tubes with­in and then care­fully weld it up again. So he did.

When at a con­fer­ence I once ac­cused him of sleep­ing through a talk — he said he had listened to the first ten minutes and that was enough and he could re­pro­duce the rest if I wanted. I knew he could.

At Not­ting Hill Car­ni­val with a few hun­dred thou­sand people, whose wild, bearded, hairy im­age was singled out and ap­peared on the 20 screens in a tele­vi­sion shop in Pet­ti­coat Lane giv­ing an Open Uni­versity lec­ture? Ob­vi­ously he had been spe­cially chosen to fit in with the reg­gae, the steel bands, the car­ni­val cos­tumes and the ganja.

The last time I saw Colin was at a con­fer­ence here in Lu­miny. Sunday lunch was at a coun­try res­taur­ant where a BMW sports car club (the vari­ous own­ers very prim and prop­er) was hav­ing an pic­nic out­ing in a field by the pool. The ex­pres­sions on some of the faces when a dishevelled Colin in his best cut-off jeans (and Bert Wi­est in his red­headed splend­our) ran off and leapt in­to the pool was something to re­mem­ber!

To re­peat, I am greatly in­debted to Colin for all I learned dur­ing my time in War­wick. And of course it was fun too! Thank you, Colin.