Timeline for What is modern algebraic topology(homotopy theory) about?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jan 20, 2016 at 18:23 | answer | added | David White | timeline score: 18 | |
| Jan 19, 2016 at 22:44 | comment | added | Ryan Budney | I'm not happy with any of the answers. I think one of the most interesting developments in modern algebraic topology is persistent homology, and the growing applications to data analysis. It has not a particularly large overlap with much of the discussion here. I think this question highlights the diversity of thought that exists in modern algebraic topology. To some, algebraic topology is a beacon of hope for generalists and foundationalists. To others it is something of the opposite: a place where some basic tools have been built that one can use to launch into other fields. | |
| Jan 19, 2016 at 21:25 | answer | added | Dmitry Vaintrob | timeline score: 13 | |
| Jan 14, 2016 at 13:33 | answer | added | David White | timeline score: 26 | |
| Jan 14, 2016 at 12:31 | answer | added | Lennart Meier | timeline score: 51 | |
| Jan 14, 2016 at 12:08 | answer | added | André Henriques | timeline score: 5 | |
| Jan 14, 2016 at 11:12 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Jan 14, 2016 at 10:12 | comment | added | Sebastian Goette | When one starts learning algebraic topology, there are nice applications, e.g. the Brouwer fixpoint theorem, invariance of dimension etc. To prove that there are no more division algebras over $\mathbb R$ than one already knows, one needs heavier tools. For the Atiyah-Singer index theorem, $K$-theory and bordism are helpful and so on. At some point, one looks for a unified treatment of these subjects, and the Brown representability theorem comes in handy. Now, one has to deal with spectra, and for me, that is where modern algebraic topology starts. But all this is already rather old stuff. | |
| Jan 14, 2016 at 9:32 | comment | added | Walter Bruce Sinclair | Tools are just tools. A hammer is "for" its nail. Homotopy theory, if it is to be a science, is just for whatever applications it can be applied to. The goal and perspective of any technology is to be, a la Heidegger, ready-to-hand. If we knew our destination in advance, we could just skip going there. | |
| Jan 14, 2016 at 8:35 | review | Close votes | |||
| Jan 15, 2016 at 4:28 | |||||
| Jan 14, 2016 at 7:52 | comment | added | Edoardo Lanari | Once you have a definition of "Homotopy theory", you can think of algebraic topology as the homotopy theory of spaces (plus extra stuff). But you also have homotopy theories of other things, according to this point of view. Just my 2 cents | |
| Jan 14, 2016 at 7:47 | review | First posts | |||
| Jan 14, 2016 at 8:31 | |||||
| Jan 14, 2016 at 7:45 | history | asked | BASIL478 | CC BY-SA 3.0 |