Friday, February 20, 2009

Long distance guidance

Here is my tribute to John Stallings on the eve of a trip to India:
I first met John Stallings in early 1967, when he visited Tata Institute of Fundamental Research to give a lecture course on Polyhedral Topology and I was asked to write up his lecture notes. I was a third year research student at that time mainly interested in Algebraic Topology and Differential Topology learnt though some unpublished notes of Samuel Eilenberg and John Milnor. I knew about John's work on Poincare conjecture and that some papers of William Browder were inspired by John's work. In prepartion for his visit, I worked through some papers of J.W. Alexander, J.H.C. Whitehead, E.C. Zeeman's notes from I.H.E.S and some papers of John on engulfing. For two months, I was in constant contact with John discussing his lectures, showing my notes, helping with shopping and a sight-seeing trip to Lonawala. He was unassuming and notes writing turned to be easy except for a couple of appendices where my reading of Whitehead helped. Most of the time, he gave me his own notes and what all I had to do was number the lemmas and add symbols on the stencils. It turned out be somewhat messy and some of the elegance of his presenation was lost in misprints. Surprisingly at the end, he offered joint authorship which I politely declined. He also gave a seminar which seemed very nice until a point when he said 'by waving hands twice, we have the result' and this was probably my introduction to Combinatorial Group Theory.. There was some correspondence soon about his lecture notes, his leaving Princeton for Berkeley and I continued to read his papers. They always seemed very elegant with neat ideas and easy to read with unpleasant technical difficulties tucked away in a half page somewhere. Slowly I found that only were his theorems useful but their generalizations too and when these did not work, one could often go back to his techniques.
Just before Stalling left Bombay, I asked whether he could suggest some problems for my thesis. I think that I wanted to prove some embedding theorems following his ideas in the lecture notes about an alternate argument in the proof of s-cobrdism theorem avoiding the Whitney trick. But what all he said was that somebody named Papakyriakopoulos did some great work. I never sudied any thing in 3-dimensional topology before and after he left, I started reading "On Dehn's lemma and Asphericity of Knots", the first paper on 3-maniflods which I read. To round it off, I read a few more papers and got stuck in 3-manifolds for a long time. Meanwhile, possibly around the end of 1967, he sent a preprint of 'Groups with infinitely many ends' which is probably my main introduction to Topological Group Theory. Though my fascination with higher dimensional topology continued, I found myself returning to Stallins papers and ideas. I do not remember any papers of mine not influenced by Stallings except possibly one on cut points which built on the impressive work of Brian Bowditch. But even here, one of Stallings students Bill Grosso, seemed to have many of the basic ideas but not proofs.
Meeting such a first rate mind at an early part of my career has inflenced me and he kept an affectionate interest in me through out my career. The acquintance with Stallings and miswriting his notes seemed to have made me a member of the Stallings community and I always felt welcomed by his students and friends.

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