Timeline for Algebraic Morse theory
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 19, 2013 at 3:45 | comment | added | Vidit Nanda | @Leon: no worries, glad to help. I wasn't kidding in my answer, it is really cool to see people (especially grad students) seriously studying algebraic or discrete Morse theory! | |
| Mar 19, 2013 at 2:37 | comment | added | Leo | @Vel Nias: It wasn't until now that I managed to go through the article and your answer. Thank you, much obliged! | |
| Mar 19, 2013 at 2:35 | vote | accept | Leo | ||
| Feb 7, 2013 at 6:34 | history | edited | Vidit Nanda | CC BY-SA 3.0 |
added 1273 characters in body
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| Jan 28, 2013 at 15:27 | comment | added | Vidit Nanda | Leon, regarding the restrictions of Kozlov and J-W: if you are interested in actual computation of homology (they are) then you need at least a pid so that you can put the matrices in smith normal form. Skoldberg also has chain complexes with a fixed basis of cells (because after all you have to impose the acyclic matching on these cells). More importantly, commutativity of the coefficient ring enables you to write the multiplicity of a path (and hence the morse boundary operator) independent of the cell ordering. I will answer your new questions soon after looking at the notation in skolberg | |
| Jan 16, 2013 at 22:30 | comment | added | Leo | Thank you very much, this helped me a lot. I'm aware that there is an analogous theory by Jollenbeck and Welker, though the fact that the results are stated in lesser generality has put me off from reading it (though I will, in the near future). Why does Jollenbeck&Welker, Minimal Resolutions via Algebraic Discrete Morse Theory, assume that all modules are free of rank $1$? Why does Kozlov, Combinatorial Algebraic Topology §11.3, assume that $R$ is commutative and modules are free of finite rank? Judging by the results from Skoldberg's article, those are all unnecessary assumptions. | |
| Jan 16, 2013 at 11:37 | history | edited | Vidit Nanda | CC BY-SA 3.0 |
added links to forman and chari's papers.
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| Jan 15, 2013 at 18:53 | history | answered | Vidit Nanda | CC BY-SA 3.0 |