Timeline for Smooth Morse function from Forman's discrete Morse function
Current License: CC BY-SA 4.0
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| Jun 24, 2020 at 20:43 | comment | added | Liviu Nicolaescu | @MikeMiller Given a triagulation the function that associates to each face its dimension is a discrete Morse function. However, if you randomly assign numbers to faces, then the probability that you get a discrete Morse function is small exponentially so as the number of faces increases. | |
| Jun 24, 2020 at 14:07 | comment | added | mme | Do you know that this is impossible for smooth Morse functions, let's say for the trivial discrete Morse function $\mu(\sigma) = \dim \sigma$? That is, is there some smooth triangulation of a smooth manifold $M$ so that there is not a smooth function $f$ on $M$ so that the barycenters of the simplices are the critical points of $f$, and the unstable manifold at a critical point is the interior of the corresponding simplex? This may be a naive question, I don't know. | |
| Jun 4, 2020 at 14:51 | history | edited | Liviu Nicolaescu | CC BY-SA 4.0 |
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| Jun 4, 2020 at 11:56 | history | edited | Liviu Nicolaescu | CC BY-SA 4.0 |
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| Jun 4, 2020 at 11:27 | history | edited | Liviu Nicolaescu | CC BY-SA 4.0 |
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| Jun 4, 2020 at 11:21 | history | answered | Liviu Nicolaescu | CC BY-SA 4.0 |