Timeline for Can we define fundamental groups functorially for non-pointed path connected topological spaces?
Current License: CC BY-SA 4.0
8 events
when toggle format | what | by | license | comment | |
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Nov 29, 2019 at 16:45 | comment | added | SashaP | @AchimKrause Yes, you are absolutely right. Thanks for the correction! | |
Nov 29, 2019 at 16:45 | history | edited | SashaP | CC BY-SA 4.0 |
added 1405 characters in body
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Nov 29, 2019 at 15:39 | comment | added | Ronnie Brown | The use of groupoids leads to "higher homotopy groupoids" which are usually "nonabelian" but to get that needs, in my view, more structure on a space than just a base point, e.g. a filtered space, or n-cube of pointed spaces. | |
Nov 29, 2019 at 15:31 | comment | added | Ronnie Brown | It's an interesting fact that the fundamental and homotopy groups are dependant on having a base point, See also this discussion:mathoverflow.net/questions/40945 | |
Nov 29, 2019 at 6:45 | comment | added | Achim Krause | They always differ for nonabelian $\pi_1$, but for an easy example just think of a perfect group. | |
Nov 29, 2019 at 6:45 | comment | added | Achim Krause | Unpointed homotopy classes $[S^1,Y]$ are given by the set of conjugacy classes in $\pi_1(Y)$, not $H_1(Y)$. (The former is the orbits of the conjugacy action of $\pi_1$ on itself in the category of sets, the latter in the category of groups (i.e. the abelianisation.) | |
Nov 28, 2019 at 22:17 | vote | accept | Zhaoting Wei | ||
Nov 28, 2019 at 21:51 | history | answered | SashaP | CC BY-SA 4.0 |