Talk:Fundamental group

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preservation of coproducts

The article claims that the fundamental group functor preserves all coproducts. This is, in general, false: a counterexample is given by the Hawaiian earring. Michael Lee Baker (talk) 05:36, 3 April 2014 (UTC)[reply]

Ouch, from the Hawaiian earring article:

G contains additional elements which arise from loops whose image is not contained in finitely many of the Hawaiian earring's circles; in fact, some of them are surjective. For example, the path that on the interval [2⁻ⁿ, 2⁻⁽ⁿ⁻¹⁾] circumnavigates the nth circle.

I guess for the coproduct to result you need base points to have contractible neighborhoods or something like that? This error goes way back to 2006. --Ørjan (talk) 09:18, 3 April 2014 (UTC)[reply]

Oh well, I've changed it to say locally contractible, I'm pretty sure that's enough. --Ørjan (talk) 09:23, 6 April 2014 (UTC)[reply]

LaTeX in descriptions has issues in dark mode

Just turn on dark mode and go through the images. If it has LaTeX in the description, the maths symbols will render with a white background. Could someone do something about it and/or give me a quick guide on how I could fix it? Nihilux (talk) 01:49, 20 August 2025 (UTC)[reply]

Fundamental group of the real projective line RP¹

The fundamental group is given here in higher dimension. I think that this article is exactly the one where the fundamental group of RP¹ has to be given.

I have read in many places on the Web that this fundamental group is Z because RP¹ and S¹ are homeomorphic topological spaces. I think that here is the right place to give (or to refer to) the indisputable solution.

( My intuition is that this fundamental group is Z x Z/2Z ... ) ~2025-29604-26 (talk) 13:06, 23 November 2025 (UTC)[reply]

After reflection I prefer the semi-direct product of Z and Z/2Z (which is isomorphic to the free product Z/2Z * Z/2Z), but certainly not Z alone. ~2025-29604-26 (talk) 15:24, 24 November 2025 (UTC)[reply]