Timeline for Every 4-manifold has a $\operatorname{Spin}^c$ Structure
Current License: CC BY-SA 4.0
16 events
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| Jul 31, 2022 at 16:47 | comment | added | LSpice | … Teichner and Vogt - All 4-manifolds have $\operatorname{Spin}^c$-structures referenced by @AntonFetisov,@DannyRuberman, and @mme; @DylanThurston's answer referenced by @GustavoGranja. | |
| Jul 31, 2022 at 16:44 | comment | added | LSpice | There seems to be no book by Morgan just called "The Seiberg–Witten equations", but there is one called "The Seiberg–Witten Equations and Applications to the Topology of Smooth Four-Manifolds" that has the result and proof you quote, so I changed the name accordingly. Names of links: @TorstenEkedahl's answer referenced by @ChrisGerig; … | |
| Jul 31, 2022 at 16:39 | history | edited | LSpice | CC BY-SA 4.0 |
`\DeclareMathOperator`; correction to name of, and link to, book; links to comments
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| Jul 31, 2022 at 14:30 | answer | added | Gustavo Granja | timeline score: 3 | |
| Jul 29, 2022 at 19:56 | comment | added | Gustavo Granja | Note that the above argument seems to use the fact that the manifold is closed, while the Teichner-Vogt argument is for an arbitrary second countable oriented $4$-manifold (only the representability of a class in $H_2(M)$ by an embedded surface is used, which can be justified geometrically, without appealing to Thom's Theorem cf. Dylan Thurston's answer to this question) | |
| Dec 4, 2018 at 19:50 | comment | added | mme | The structure of Teichner's webpage has changed, and the original link is now broken.The most up-to-date version of Danny's link is people.mpim-bonn.mpg.de/teichner/Math/ewExternalFiles/spin.pdf | |
| Apr 14, 2017 at 14:12 | comment | added | Danny Ruberman | Another proof along these lines is given in a short note of Teichner and Vogt, people.mpim-bonn.mpg.de/teichner/Papers/spin.pdf. You might find the exposition there helpful. | |
| Apr 14, 2017 at 11:12 | answer | added | Mark Grant | timeline score: 5 | |
| S Apr 14, 2017 at 3:38 | history | suggested | jdk3264 | CC BY-SA 3.0 |
Added more clarification of question.
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| Apr 14, 2017 at 3:22 | review | Suggested edits | |||
| S Apr 14, 2017 at 3:38 | |||||
| Apr 12, 2017 at 21:07 | comment | added | Anton Fetisov | Dimension 4 is required because any proof rests either on the Poincare duality (in compact case) or on the intersection form on 2-cohomology in general. Note that you also need orientability. I didn't read the paper you cite, but perhaps this paper will help. | |
| Apr 12, 2017 at 5:22 | review | Close votes | |||
| Apr 12, 2017 at 11:09 | |||||
| Apr 12, 2017 at 5:06 | comment | added | Ryan Budney | Your question is rather vague. Could you write it up in a way that doesn't require readers to go somewhere else? | |
| Apr 12, 2017 at 1:32 | comment | added | jdk3264 | Thanks for the comment. Yes, I am familiar with the result of Thom, but I'm not aware of its extension to manifolds with a G-structure in Q1. Torsten's answer is nice but it seems to indicate that we didn't need the torsion condition at all in Q2. | |
| Apr 11, 2017 at 23:01 | review | First posts | |||
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| Apr 11, 2017 at 23:01 | history | asked | jdk3264 | CC BY-SA 3.0 |