Timeline for Analogue of singularity theory in other categories
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 20, 2013 at 15:10 | answer | added | Vidit Nanda | timeline score: 1 | |
| Jul 20, 2013 at 14:37 | comment | added | Vidit Nanda | @AndrásSzűcs The Cappell-Shaneson paper from my comment deals exclusively with the case dim target = 2 + dim source, which is a (very?) special case of your general interest. I will write a few words on PL Morse theory as an answer because it is difficult to format math in comments. | |
| Jul 20, 2013 at 14:22 | comment | added | András Szűcs | Thanks Daniel. I can see that MO is really a useful thing. | |
| Jul 20, 2013 at 12:53 | comment | added | Daniel Moskovich | For the PL category, you might be interested in the answers to this question: mathoverflow.net/questions/56597/… | |
| Jul 20, 2013 at 7:58 | comment | added | András Szűcs | Thank you Vidit. I would need this singularity theory for positive codiension maps (dim target > dim source). But thanks for mentioning PL Morse theory. Can you tell me in two sentences what it is? | |
| Jul 19, 2013 at 23:53 | comment | added | Vidit Nanda | There has been a considerable amount of work in PL Morse theory which has two flavors: Bestvina's PL Morse theory and Forman's Discrete Morse theory. If you are interested in singularities of $f:X \to Y$ for $Y$ different from the real line, the literature is extremely sparse. But see Cappell and Shaneson's paper on singularities of co-dimension 2 PL embeddings: jstor.org/stable/1971003 | |
| Jul 19, 2013 at 22:25 | history | edited | Kevin Ventullo | CC BY-SA 3.0 |
Fixed typo
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| Jul 19, 2013 at 22:09 | history | asked | András Szűcs | CC BY-SA 3.0 |