Celebratio Mathematica

We gath­er here be­low the trib­utes for An­drew Ran­icki writ­ten by col­leagues after his death in 2018 and shared on the “Alg-Top” list­serv group, an on­line com­munity of to­po­lo­gists. We de­cided to present them to­geth­er since they re­flect An­drew’s role with­in this com­munity: sev­er­al com­ment on how read­ily An­drew as­sisted oth­ers in an­swer­ing ques­tions, and his gen­er­ous (and more gen­er­al) con­tri­bu­tions to the qual­ity of dis­cus­sion on the Alg-Top list­serv it­self are spe­cific­ally re­membered by Don Dav­is, the list­serv own­er.

– Ed­it­or

An­drew Ran­icki cre­ated unique links between al­gebra and geo­met­ric to­po­logy. He was an en­thu­si­ast of math­em­at­ics and a won­der­ful per­son. He will be missed!

Dear all,

We were sur­prised and saddened very much by the news of An­drew’s oh so un­timely death. We were vis­it­ing Ida and him for the week­end right be­fore and just wanted to share our ex­per­i­ence a little.

We were wel­comed with the same warmth and heart­felt joy, that seems to be present in every re­col­lec­tion of a vis­it to their house, even dur­ing this dif­fi­cult time. An­drew’s in­cred­ibly in­fec­tious laughter could still be heard far and wide (he in­sisted on us watch­ing you­tube.com/watch?v=9d­fWzp7rYR4, un­able to keep his com­pos­ure 10 seconds in) and his spir­it was quite un­broken as well: He in­vited us to the hos­pit­al with him for what was sched­uled as a routine blood test, where we dis­cussed new and old de­vel­op­ments in L-the­ory quite fer­vently (much to the amuse­ment of the nurses and oth­er pa­tients). A math­em­atician to the last…

Dur­ing the last year An­drew had a tre­mend­ous ef­fect on our re­search ef­forts, with Skype ses­sions hap­pen­ing al­most every week and a lot of know­ledge and good ad­vice com­ing our way (as well as the oc­ca­sion­al pic­ture, video snip­pet or oth­er oddity that he al­ways de­lighted in shar­ing).

We shall dearly miss talk­ing to him, both math­em­at­ic­ally and even more about the world in gen­er­al.

Dear friends,

Like Frank Con­nolly I met An­drew for the first time at the 1972 Seattle K-the­ory con­fer­ence. As a mat­ter of fact, An­drew sent me af­ter­wards the pic­ture of people at­tend­ing the con­fer­ence. This pic­ture may not be known to every­body.

There is no point to tell more about An­drew’s charm­ing per­son­al­ity and math[emat­ic­al] in­flu­ence as many did so well. Al­though I was not too close math­em­at­ic­ally to An­drew, I want to em­phas­ize that he was al­ways ready to an­swer im­me­di­ately my ques­tions. For in­stance, he poin­ted to me a pa­per of Clauwens about sur­gery very much re­lated to my quer­ies at that time.

Polit­ic­ally, An­drew (with Wolfgang Lueck) warned us many years ago about the poor man­age­ment of the Journ­al of K-The­ory. Un­for­tu­nately, we waited too much to fol­low his ad­vice and to cre­ate a new Journ­al with a good basis.

[I] first heard the name “An­drew Ran­icki” in 1981 when I fell un­der the tu­tel­age of Bill Richter as a sopho­more at North­west­ern. Bill was giv­en an un­der­gradu­ate thes­is prob­lem by An­drew when he was at Prin­ceton that in­volved clas­si­fy­ing high di­men­sion­al knots in the meta­stable range. As part of the pro­ject, Bill had to de­vel­op a ho­mo­topy the­or­et­ic ver­sion of the Blanch­field pair­ing and the lat­ter was an ap­plic­a­tion of what Adam’s called “Ran­icki du­al­ity.” This du­al­ity is ver­sion of Span­i­er–White­head du­al­ity in the cat­egory of spaces with free \( \pi \)-ac­tion (here \( \pi \) can be any dis­crete group).

I may have first en­countered An­drew in the flesh in 1982 at the North­west­ern ho­mo­topy the­ory meet­ing (I’m not sure if I did, and I am not sure if he was there). However, my first con­tact with An­drew oc­curred in the early 1990s at Ober­wolfach. From that point on­ward un­til about five years ago we main­tained a steady flow of cor­res­pond­ence.

I nev­er wrote a pa­per with him, but I can say that a lot of the tech­no­logy I im­ple­men­ted came from him. He was al­ways very sup­port­ive of my re­search. Here are a few snip­pets: an ex­ten­sion of Ran­icki du­al­ity to to­po­lo­gic­al groups ap­pears in quite a lot of my pa­pers. Also, the \( Z/2 \)-equivari­ant stable Hopf in­vari­ant (Crabb and Ran­icki) also ap­pears in sev­er­al of my pa­pers; I learned a lot about the lat­ter from talk­ing to An­drew. After I had pro­duced the re­quis­ite em­bed­ding the­or­ems in the Poin­caré du­al­ity cat­egory, An­drew pushed me to write down a defin­it­ive treat­ment of Poin­caré sur­gery (which I failed to muster the cour­age to do: I was al­ways stuck between de­cid­ing on the Wall ap­proach or the Ran­icki ap­proach. Each has its ad­vant­ages and dis­ad­vant­ages).

I vis­ited An­drew and Ida sev­er­al times in the late 1990s and early 2000s. They were phe­nom­en­al hosts, and their gen­er­os­ity was fam­ous in the math world. I par­tic­u­larly re­call vis­it­ing them with my wife and first child — that would have been in Au­gust 1999 dur­ing the Fringe Fest­iv­al. We spent a won­der­ful time in their house for a few weeks.

There are two fi­nal memor­ies I wish to con­trib­ute that I think provide some of the “fla­vor” of An­drew:

The first of these was An­drew’s unique way of enun­ci­at­ing cer­tain words. One of these was his pro­nun­ci­ation of “ab­so­lutely.” When he spoke it, it had an amaz­ing ring, with stresses on a deep, sol­id “o” and “u.”

The second memory is an an­ec­dote:

Upon An­drew’s com­ple­tion of Ex­act Se­quences in the Al­geb­ra­ic The­ory of Sur­gery (aka to some as the yel­low pages of sur­gery, maths.ed.ac.uk/ aar/books/ex­act.pdf), An­drew’s fath­er, the great lit­er­ary crit­ic, Mar­cel Reich-Ran­icki, asked his son, “Whom are you at­tack­ing in this book?” An­drew tried to ex­plain to his fath­er that one doesn’t typ­ic­ally at­tack oth­er math­em­aticians in a math­em­at­ic­al manuscript. But alas, Mar­cel didn’t seem to com­pre­hend that.

Dear friends,

I met An­drew for the first time on my first con­fer­ence in Ober­wolfach in the fall 1983.

I had not yet fin­ished my PhD and he wanted to know what I was do­ing. I re­mem­ber that I was very sur­prised and not used to that such an es­tab­lished math­em­atician was in­ter­ested in the work of a PhD stu­dent he had nev­er met be­fore.

Dur­ing the con­ver­sa­tion he real­ized and told me that hid­den in my thes­is was a solu­tion to a prob­lem, he and oth­ers had worked on in a spe­cial case and whose gen­er­al solu­tions was presen­ted in my thes­is. It is about trans­fer al­geb­ra­ic K-the­ory. At that time, without in­ter­net and email, young math­em­aticians were work­ing in com­plete isol­a­tion and such hints and sup­port were ex­tremely valu­able. In par­tic­u­lar An­drew was very en­cour­aging, and one of the first math­em­aticians who did not work in Goet­tin­gen and to whom I could talk about my pro­jects.

In 1985 he in­vited me to a very pleas­ant and fruit­ful stay in his house in Ed­in­burgh, which was the be­gin­ning of two pa­pers we wrote to­geth­er and of a long pro­fes­sion­al and per­son­al re­la­tion­ship.

There were many in­stances, where we met and had a lot of fun to­geth­er. I could con­tin­ue telling nice stor­ies about An­drew, which would re­flect his warm per­son­al­ity, but every­body knows how kind and en­ter­tain­ing An­drew was so that there is no need to do that.

One high­light was his six­tieth birth­day con­fer­ence, which I or­gan­ized in Muen­ster. An­drew’s fath­er came also and gave a very nice pub­lic speech.

An­drew is the first math­em­atician of the gen­er­a­tion that edu­cated and sup­por­ted me dur­ing my ca­reer to have passed away. Whom shall we ask ques­tions about al­geb­ra­ic sur­gery in the fu­ture?

When you en­counter such a prob­lem, we all had the re­flex to write an email to An­drew, and we were used to get­ting an an­swer very quickly.

Four weeks ago An­drew and I had a long Skype con­ver­sa­tion. I had the im­pres­sion that he was in good shape. We had even made plans for him to come vis­it Bonn. You can ima­gine that it was a shock for me when I was in­formed that he passed away. I must ad­mit that it has been hard for me to ac­cept that I will nev­er talk to him again.

An­drew, I am miss­ing you.

In the days when nonsimply con­nec­ted sur­gery was still young, An­drew, an as­sist­ant pro­fess­or at the time, was a warm and en­thu­si­ast­ic pres­ence at Prin­ceton. I was then a tem­por­ary mem­ber at the In­sti­tute for Ad­vanced Study. Our paths di­verged long ago, An­drew in sur­gery and me in ho­mo­topy the­ory, but I re­mem­ber him fondly from those days. He lives in my memor­ies and I will miss him.