Timeline for How to compute fundamental groups of closed surfaces without using Van-Kampen theorem?
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| Mar 16, 2020 at 5:25 | comment | added | Dmitri Pavlov | @ConnorMalin: No, it does not. For example, you can use the CW-approximation theorem to represent elements in the fundamental group(oid) as cellular maps from [0,1] to the 1-skeleton and homotopies between them as cellular maps from a bigon to the 2-skeleton. From there you can deduce a presentation of the above type. And for simplicial sets it's even easier, since maps are already simplicial. | |
| Mar 15, 2020 at 22:58 | comment | added | Connor Malin | Doesn’t knowing this gives a presentation of the fundamental groupoid require van Kampen? | |
| Mar 15, 2020 at 22:24 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |