Timeline for Historical transition from classical homotopy to modern homotopy theory
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Jan 21, 2023 at 18:22 | history | edited | Paladin | CC BY-SA 4.0 |
edited body
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| Jun 12, 2022 at 12:11 | answer | added | Peter May | timeline score: 3 | |
| Jun 12, 2022 at 11:39 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
corrected some minor typos and added a top-level tag
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| Jul 1, 2011 at 16:22 | comment | added | The Mathemagician | @KConrad Just spotted the error.Obviously,I meant a nice,IN-expensive edition for students.A Dover edition of Whitehead's book for under 25 dollars would be awesome. | |
| May 3, 2010 at 14:33 | answer | added | Lennart Meier | timeline score: 12 | |
| May 3, 2010 at 13:44 | comment | added | Tim Perutz | My (non-expert) impression was that a main catalyst for the trend towards abstraction in algebraic topology was Quillen's discovery of the relation between complex cobordism and formal groups. This offered the possibility of building new cohomology theories algebraically rather than geometrically, by a mechanism which is still apparently useful in understanding homotopy groups (see e.g. the famous recent Hill-Hopkins-Ravenel paper). | |
| May 3, 2010 at 8:47 | comment | added | Jeffrey Giansiracusa | I'd just like to point out that model categories don't really offer an 'alternative approach' to homotopy theory. They are an axiomatization of the techniques that had already been developed for working with spaces or simplicial sets, and the idea was to use them as a guide for applying the same yoga in other settings. | |
| May 3, 2010 at 8:42 | comment | added | Pietro | "Algebraic topology is too big to have a coherent history." What? Entire civilizations have "coherent histories" that can be communicated in meaningful and useful ways. Surely algebraic topology, and even all of mathematics, being infinitely less complex, is amenable to similar treatment? | |
| May 3, 2010 at 5:31 | comment | added | KConrad | OK, then the comment is directed to Andrew. (I'm tempted to make the edit directly, but I'd rather have the person who wrote that do it in this case.) | |
| May 3, 2010 at 5:29 | comment | added | S. Carnahan♦ | @KConrad, those were AndrewL's words, not Yemon's. | |
| May 3, 2010 at 3:19 | comment | added | KConrad | Yemon, you write that you want to make the book available as a "nice expensive edition". Umm.... | |
| May 3, 2010 at 1:52 | comment | added | Tyler Lawson | One point to make is that Whitehead's book wasn't necessarily the standard approach to teaching homotopy theory when it was published, either, particularly the amount of time devoted to spectral sequences. (See Adams' review at projecteuclid.org/euclid.bams/1183545223). It is also not obsolete. It simply has a different emphasis (e.g. many modern texts don't devote much time the classical Lie groups). | |
| May 2, 2010 at 23:40 | answer | added | Scott Carter | timeline score: 1 | |
| May 2, 2010 at 22:48 | comment | added | Charlie Frohman | Algebraic topology is too big to have a coherent history. The bomb dropped in 1945 when Eilenberg and MacLane wrote the "book" and we have been reacting ever since. | |
| May 2, 2010 at 22:09 | history | edited | Yemon Choi | CC BY-SA 2.5 |
fixed markdown mis-format
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| May 2, 2010 at 20:50 | history | asked | The Mathemagician | CC BY-SA 2.5 |