Answer by Omar Antolín-Camarena for Why are we interested in the Fundamental...
I'm very fond of Ronnie Brown's proof of the Jordan curve theorem using the groupoid version of the van Kampen theorem. I find it easier to understand and reproduce than other comparably elementary...
View ArticleAnswer by Ronnie Brown for Why are we interested in the Fundamental Groupoid...
I confess, in 1965 or so, I first thought that the version of the SvKT (Seifert-van Kampen Theorem) for the fundamental groupoid enabled us to get rid of base points. But then I wanted to calculate the...
View ArticleAnswer by Tim Porter for Why are we interested in the Fundamental Groupoid of...
The simplest natural example is to use the van Kampen theorem (in Ronnie Brown's version) to work out the fundamental group(oid) of the circle. The details are in his book Topology and Groupoids...
View ArticleWhy are we interested in the Fundamental Groupoid of a Space?
The classical version of the van Kampen theorem is concerned about the fundamental group of a based space. In fact, it says that the functor $\pi_1$ preserves certain types of pushouts in $Top_*$.There...
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