Thursday, October 12, 2023
Old age blues
Last few weeks I have been thinking of accessibility of finitely presented groups proved by Martin Dunwoody in 1983. I thought about it around 1974 and had the right ideas. But at that time algebra was not really my area and I gave up on some good problems after getting the right ideas. I also thought that may be one can use minimal surfaces but knew very little of the area. I gave a talk in Stoney Brook around 1979-80about it and Gromov was in the audience. Then after coming to Melbourne, in random browsing of our departmental library, I saw a volume in honour of some mathematician, may be I.M. Gelfand, and there was a paper by Gromov proving accessibility using minimal surfaces in higher dimensions. I even remember he used dimensions bigger than 6. I have a visual memory of the book and the paper.
Recently, I started thinking about it since Peter Scott with me and two others developed an analogue of minimal surfaces for groups. I tried to ask friends about it but nobody knows about Gromov’s proof. Meanwhile our departmental library closed and the books were sent other libraries in the University. I cannot find the book.
I wonder what is happening. Did I imagine all this. My working on mathematics is very haphazard. I basically learnt by myself. It was more passion than ambition. So there are lot of gaps in my knowledge of the areas I work. I often follow the general outline and try to fill the gaps later. For example, I did not read some of Waldhausen’s papers in 1969 but found simple proofs around 2002. I do not know whether it is one of those things or whether I really imagined the whole thing. I wrote to Gromov yesterday and I do not know whether he will reply.
It surprises me that i did and can do some mathematics. I have no confidence in my abilities or any ambition. But if some thing bugs me, I keep thinking about it sometimes for years. I have also been lucky with collaborators, that after the age of 45 or so. But I did a few interesting things before. Anyway, I am puzzled by how I have been able to do some mathematics and even made a living given that I come from a farming family.
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GROMOV-FOLIATED PLATEAU PROBLEM, PART I:
MINIMAL VARIETIES
https://sci-hub.ru/10.1007/bf01895417
GROMOV-FOLIATED PLATEAU PROBLEM, PART II:
HARMONIC MAPS OF FOLIATIONS
https://sci-hub.ru/10.1007/bf01896204
https://libgen.rs/scimag/?q=%22Foliated+Plateau+problem%22
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