Timeline for Algebraic topology and homotopy theory with simplicial sets instead of topological spaces
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 25, 2021 at 8:03 | comment | added | Tim Porter | Thanks to Denis, you have the link. Sorry for not giving the link myself, but my reason for not giving you all the details was to encourage you to search online to find that paper, as I have found that that way you sometimes chance on a paper other than the one you are searching for, but which is more to your taste, fits your background better, etc. and which is potentially more useful to you, than the one that was suggested. BTW searching on 'Curtis' and 'simplicial' gives you a link to the nLab entry that gives lots of other links. ncatlab.org/nlab/show/simplicial+homotopy+theory | |
| Nov 24, 2021 at 16:22 | comment | added | Denis Nardin | @user469290 sciencedirect.com/science/article/pii/0001870871900156 | |
| Nov 24, 2021 at 15:08 | vote | accept | user469290 | ||
| Nov 24, 2021 at 15:07 | comment | added | user469290 | @TimPorter Which paper by Curtis? How am I supposed what "the classic paper" is? | |
| Nov 24, 2021 at 13:06 | comment | added | Denis Nardin | @TimPorter Yeah I was bundling that with "modern shape theory", I wanted mainly to exclude Borsuk shape theory (which I think was done mainly with topological spaces), perhaps I went overboard :). | |
| Nov 24, 2021 at 10:48 | comment | added | Tim Porter | I would add the classic paper by Curtis to the list of places that the original contributor could look. | |
| Nov 24, 2021 at 10:46 | comment | added | Tim Porter | @Denis Nardin. That was true as well in now classical shape theory, an area that does not get as good mention as it deserves. e.g. see the classic lecture notes by Edwards and Hastings. Creative use of simplicial sets in Shape and Strong Shape was there from the start. | |
| Nov 24, 2021 at 5:59 | answer | added | John Palmieri | timeline score: 8 | |
| Nov 24, 2021 at 3:04 | history | became hot network question | |||
| Nov 23, 2021 at 20:38 | comment | added | Denis Nardin | @TomLeinster Actually, using modern shape theory, I would argue that simplicial sets are excellent for studying the homotopy theory of pathological spaces :). You just gotta use them in a creative way... | |
| Nov 23, 2021 at 20:36 | answer | added | Denis Nardin | timeline score: 16 | |
| Nov 23, 2021 at 20:31 | review | Close votes | |||
| Nov 28, 2021 at 3:07 | |||||
| Nov 23, 2021 at 20:09 | comment | added | Tom Leinster | It's a fair question, but there's a circular or self-referential aspect to this kind of thing. Many people would more or less define mainstream algebraic topology to be that which can be captured by simplicial sets. If one were to argue that simplicial sets are an inadequate tool for the algebraic topology of certain non-standard classes of spaces (e.g. non-Hausdorff, or totally disconnected, or fractal) then the reply would probably be "that's not what I mean by algebraic topology". The subject is defined by its standard tools, of which simplicial sets are one. | |
| Nov 23, 2021 at 19:13 | comment | added | Benjamin Steinberg | If you only care about things to homotopy then bigger experts than I will say all you need is simplcial sets and say stuff about model categories and Quillen equialence. If you cannot replace maps by homotopy equivalent maps you lose information. A good reference to simplicial sets is Peter May's classic Simplicial Objects in Algebraic Topology | |
| S Nov 23, 2021 at 19:04 | review | First questions | |||
| Nov 23, 2021 at 19:20 | |||||
| S Nov 23, 2021 at 19:04 | history | asked | user469290 | CC BY-SA 4.0 |