2018年02月23日

Andrew Ranicki passed away.

Andrew Ranicki passed away on February 20. He was 69 years old. He was an expert on algebraic theory of "surgery" (aka algebraic L-theory). He recently published a new book, titled "The Geometric Hopf Invariant and Surgery Theory", jointly with Prof. M. Crabb of Aberdeen. I have a copy of the book on my desk now. The book is dedicated to his grandson Nico Marcel Vallauri. See the picture. Nico is a son of Andrew's daughter, Carla. The picture was taken by her.

Hopf_Nico.jpg

I owe a lot to him. My Ph.D thesis (1982) completely depends on his fundamental works on surgery.

During the 80's I was thinking about "squeezing" of "quadratic complexes" of Ranicki. I thought I could prove a squeezing result for chain complexes using a sort of Alexander trick for chain complexes, and gave a talk at a conference at University of Notre Dame. Andrew immediately found that something was seriously wrong with my argument, and he changed the topic of his talk and gave a counter example to what I claimed! But he was very kind and tried to be very vague about my errors, so most people there did not understand the point of his talk. He privately explained his argument to me in detail, and told me to come and work in Edinburgh. That encouraged me a lot.

I did not forget his words and spent the academic year 1990/91 in Edinburgh with my family. Andrew was so kind and prepared everything for me and my family. On our first evening in Edinburgh, my younger son Hisashi (Yamasaki Hisashi) had a fit and hospitalized. Andrew helped us a lot.

This one year was very fruitful for me mathematically. Andrew described his ideas to me very clearly, and I could understand what he wanted to do very quickly. But I was rather slow after that and it took me 5 years to materialize the "controlld K" paper and it took me 10 more years to materealize the "controlled L" paper. After finifhing them I was very tired, but it was worth working on it. Later, Guentner, Tessera , and Yu used our controlled K and L papers to prove good results related to Novikov Conjecture. I was very happy, and I believe Andrew was also very happy about it!

Besides mathematics, I also learned plainTeX from him. (Eventually we all moved to AMS-LaTeX later.)

As for squeezing problem, Erik Pedersen insisted that L-theory squeezing should hold true without any K-theoretic assumtions and actually gave a proof when the control space is a circle, around 1998. I was rather skeptical, because of my earlier failure, but Erik was very enthusiastic so I kept the problem in my mind for several years without any success. But around 2003, I could come up with an idea of inductive application of Alexander tricks, and we could give a proof of a squeezing theorem for controlled L-theory. In the proof we used the ingredients of controlled K-theory and L-theory papers of Ranicki-Yamasaki. In the 80's, I did not know the technology which had been already developed by Andrew.

I have been naively imagining that Andrew would live very long, because his parents lived very long and Andrew was always full of energy. So the news of his death was very shocking to me. I will never forget the day "February 20", because it is my birthday and also a birthday of John Milnor who was one of the pioneers of surgery theory.

Thanks a lot, Andrew! Please rest in peace.

posted by dunno at 12:50| Comment(0) | TrackBack(0) | 思い出
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