Category Theory, Applications to Algebra, Logic, and Topology: Proceedings, Gummersbach, FRG, 1981

Lectures notes ...
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Dokumenty k polske okupaci v ukrajinskem uzemi halicskem. Rok az do prosine I Proceedings Catalog of Copyright Entries. Air Pub. Report of the British Mission to Japan. Moore started out by writing out his axioms on the board. Something like five minutes went by, and there was no sound except this chalk on the blackboard.

Moore turned around slowly and looked at Lefschetz and said, "If you would read what I have written on the board, you wouldn't need to ask your question". You could tell when Lefschetz was getting angry because the back of his neck would get pink. Lefschetz repeatedly asked questions, which we knew was just Lefschetz's style, but every one of these Moore regarded somehow as being a planted barb, so he would come back very hard in some scornful way. Alexander actually tried to pitch in and help Lefschetz a bit, but on points Moore won easily.

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Again he sat where we could watch the back of his neck, and it would get red and then the colour would recede, but he didn't say a word. As far as I couldjudge, everybody went out of his way to show interest and concern and respect towards Moore. But this heckling was just a standard thing with Lefschetz'. No picture of the golden age of Princeton would be complete without some indication of how it appeared to the students. For this we are fortunate to have the letters written by Steenrod to Wilder after he arrived in Princeton as a graduate student.

Steenrod, I recall, was a native of Ohio who studied at Ann Arbor under Wilder, and these letters give a vivid picture of life at Princeton as seen through the eyes of a graduate student. While Tucker, in his reminiscences, looks back on events that happened forty years earlier, Steenrod is describing his experiences at the time. We see how Princeton shaped Steenrod's mathe- matical development, converting him from point-set topology to combinatorial topology. The following extracts from this material, which have not previously been published, give a vivid picture of topology at Princeton in the mid-thirties, not long after the Enzyklopdie artic1e of Tietze and Vietoris was published.

At the end of the last letter, as we shall see, Hurewicz arrives, bringing modem homotopy theory to Princeton. Not long afterwards Alexander ceased to be active in research, and a few years later Lefschetz' interests moved away from topology in the direction of differential equations. Steenrod retumed to Princeton as a faculty member, after aperiod back in the midwest.

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Fox, another former student of Lefschetz, was also recruited to the faculty, and together they gradually took over the leadership of the topology group at the university. At the Institute Morse was joined by Whitney from Harvard. However the later history of topology at Princeton is another story, for which I refer the reader to Borel [7]. It must be that I'm enjoying it all, but I've really not had the opportunity to sit down and come to a conc1usion on the matter - or maybe I don't want to This is a leisurely joint - but I don't imagine I'm telling you anything.

It took them two weeks to get started.

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It was a month before they put me to work. My job breaks into two parts. The library work is no burden. The only things the place lacks are spittoons - a fellow can't have his chew. The editorial work is a bit different. Just before the proofs are sent out i. Greek underlined in red, German in green, etc The main thing 1 don't like about it is that there isn't enough time allowed for me to read the papers on topology.

He made no comment except to recommend seeing Lefschetz, who, he was sure, would have something to say about it. A few days later Tucker stopped me and said Zippin had asked ab out me. So 1 set about looking Zippin up. The first step was to see Miss Blake. When this failed she caIled him on the phone, it was about He's a pretty sweIl sort of person.

We talked for over two hours. Among other things, he strongly recommended my going after the recent efforts of Pontrjagin. He gave loaned, 1 mean me a set of galleys of Pontrjagin's paper in the April issue of the Annals. This paper, by the way, I've just about finished. It's nice, easy reading with some red-hot theorems. When the October Annals appeared 1 skimmed through the Pontrjagin paper on the duality theorem to see how he applied his results.

Lecture notes in mathematics

It doesn't seem to me as though there is any other theorem in mathematics quite as beautiful as the one he's got. He first gave us a short lecture and then began on us one by one and recommended courses.

He invariably insisted on projective geometry; so when it came to my turn 1 swore up and down that 1 was weIl versed in the subject. So he finally agreed that perhaps 1 was weIl enough prepared to take his topology course. About a week later someone, perhaps Tucker, reminded Lefschetz that 1 was Prof.

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Wilder' s pet, for he stopped me after one of his lectures and introduced me to Mr. Wallman and inveigled me into collaborating with Mr. Wallman in writing up his Lefschetz's lecture notes for the topology course. Heaven knows why this is necessary. As yet it doesn't appear that he is doing this. He did attempt to introduce the notion of chains with coefficients which are rational numbers modulo 1. But he got stuck when someone pointed out that they didn't form a ring i.

The next day he insisted that it was all right since all he needed was that they should form a group. Everyone is still suspicious of the matter.