Timeline for Easier ways to compute homology/cohomology by adding extra structure
Current License: CC BY-SA 4.0
13 events
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| Oct 17, 2019 at 11:26 | comment | added | Praphulla Koushik | @RyanBudney That sounds reasonable.. Do you happen to know if fixing a connection on $TM\rightarrow M$ gives a cochain complex $\mathcal{S}$ that is a subcomplex of $\{\Omega^k(M)\}$ that gives same cohomology? | |
| Oct 17, 2019 at 5:46 | comment | added | Ryan Budney | Often times computing homology via a CW-structure, triangulation or a Morse function are equally difficult. For example, with triangulations your attaching maps are simpler, but you have far more of them than with a CW-complex. Is one "easier" than the other? This is analogous to the trade-off between runtime and memory usage in software optimization. A slower algorithm that uses less memory is best if you have little memory, but a fast algorithm that's a memory hog could be better if you have access to unlimited memory. | |
| Oct 17, 2019 at 4:42 | history | edited | Praphulla Koushik | CC BY-SA 4.0 |
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| Oct 16, 2019 at 5:17 | comment | added | Praphulla Koushik | @StevenLandsburg I do not know how my comment has reached :) I do not even understand how it is useful to others. I want to improve so expecting some response from some one who has some thing to say about what I can improve.. There was no intention of rudeness (if it sounds so)... :) | |
| Oct 15, 2019 at 23:27 | comment | added | Steven Landsburg | "What is the use of that downvote if it does not teach me anything?". Were you unaware that a thing can be useful to others even if it's not useful to you? (For the record, I am not the downvoter.) | |
| Oct 15, 2019 at 3:24 | comment | added | Praphulla Koushik | Read reach as teach | |
| Oct 15, 2019 at 2:32 | comment | added | Praphulla Koushik | Please let me know reason for downvote.. what is the use of that downvote if it does not reach me anything | |
| Oct 14, 2019 at 7:40 | history | edited | Praphulla Koushik | CC BY-SA 4.0 |
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| Oct 14, 2019 at 7:40 | answer | added | Lennart Meier | timeline score: 4 | |
| Oct 14, 2019 at 6:35 | comment | added | Praphulla Koushik | @LennartMeier I do not know much about Morse function.. Is it reasonable to ask a manifold has a Morse function, I mean does it happens quite often that a manifold I choose has a Morse function.. please see if you can add it as an answer.. can you suggest some references, I am already seeing Wikipedia page.. | |
| Oct 14, 2019 at 6:28 | history | edited | Praphulla Koushik | CC BY-SA 4.0 |
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| Oct 14, 2019 at 6:27 | comment | added | Lennart Meier | On a manifold, I might have a Morse function procuding the Morse chain complex. On a simplicial complex I might have a discrete Morse function, which can drastically simplify the simplicial chain complex. | |
| Oct 14, 2019 at 6:07 | history | asked | Praphulla Koushik | CC BY-SA 4.0 |