Timeline for How to compute fundamental groups of closed surfaces without using Van-Kampen theorem?
Current License: CC BY-SA 4.0
6 events
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| Mar 16, 2020 at 20:14 | comment | added | Lee Mosher | For $S^2$, an argument which uses the Lebesgue Number Lemma directly is pretty simple (that lemma, of course, is the main technical tool of a "Van Kampen style argument"). | |
| Mar 16, 2020 at 4:19 | comment | added | Ryan Budney | It's been a long time, but I recall the textbook by Singer and Thorpe takes this perspective. | |
| Mar 16, 2020 at 2:31 | history | edited | Nicholas Kuhn | CC BY-SA 4.0 |
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| Mar 16, 2020 at 1:22 | comment | added | Connor Malin | Or just cellular approximation | |
| Mar 16, 2020 at 1:10 | comment | added | Thomas Rot | Simply connectedness of the twosphere might be proven using sard. A continuous curve is homotopic to a smooth one, its image misses at least a point by Sard. Call such a choice of point $x$. One can contract the curve to $-x$. | |
| Mar 16, 2020 at 0:22 | history | answered | Nicholas Kuhn | CC BY-SA 4.0 |