Timeline for Reference request and prerequisites for understanding the Sphere Theorem and the Loop Theorem in 3-manifold theory
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 27, 2023 at 16:21 | vote | accept | ZSMJ | ||
| Sep 27, 2023 at 13:12 | comment | added | Sam Nead | Andrew Casson has written lecture notes proving the sphere, disk, annulus, and torus theorems using "PL minimal surface theory" (following Jaco and Rubinstein). The notes can be found here: homepages.warwick.ac.uk/~masgar/casson.html | |
| Sep 27, 2023 at 4:44 | answer | added | Ian Agol | timeline score: 2 | |
| Jul 21, 2023 at 23:43 | comment | added | Greg Friedman | Sounds like mostly you're missing material from a slightly more advanced algebraic topology course. You should be able to find that material nicely explained in Hatcher's Alegraic Topology or Munkres's Elements of Algebraic Topology. Of course you may need other things as well, but those will certainly cover Universal Coefficients and Poincare Duality. | |
| Jul 19, 2023 at 18:56 | comment | added | Igor Belegradek | The usual method of reading research papers is to pick up necessary background as you go. This is normal. Don't let this discourage you. | |
| Jul 19, 2023 at 15:47 | comment | added | ZSMJ | @IgorBelegradek I tried reading it from the mentioned sources but I am encountering concepts like Poincare Duality and Universal Coefficient Theorem etc. that I am unfamiliar with so I have to repeatedly go back and look these up. My background in 3 manifold theory and differential topology is limited which I'm trying to fix by reading John Lee's intro to topological and smooth manifolds. I was hoping to find a reference which would be dedicated to these two theorems and self sufficient in terms of prerequisites. | |
| Jul 19, 2023 at 13:49 | comment | added | Igor Belegradek | Wouldn't it be easier to just read the proofs and see what (if anything) you are missing? Sounds like you already have sufficient background. | |
| Jul 19, 2023 at 10:23 | comment | added | ZSMJ | Also posted on MSE math.stackexchange.com/q/4733233/116321 | |
| Jul 19, 2023 at 10:23 | history | asked | ZSMJ | CC BY-SA 4.0 |