Timeline for Fundamental group of the line with the double origin.
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Jun 22, 2017 at 10:25 | comment | added | Ronnie Brown | The arguments using many base points allows one also to do, for example, the case of two copies of the real line identified at non integral points. . See also mathoverflow.net/questions/40945/… | |
| Nov 8, 2013 at 18:46 | comment | added | Ronnie Brown | The argument is pretty well the same as 6.7.5 of "Topology and Groupoids" , an argument which appeared in the 1968 and 1988, differently named, editions. You need 2 base points, namely the unidentified points. My starting point was to find a version of the van Kampen theorem which computes as a special case the fundamental group of the circle, which is, after all, THE basic example in algebraic topology. This version also has a corollary an example given in van Kampen's paper, i.e. when $X= U \cup V$ and $U \cap V$ has $n$ path components (see 8.4.1 of T&G). | |
| May 22, 2010 at 15:20 | comment | added | Kevin H. Lin | There is also the book "Topology and Groupoids" by Ronald Brown. | |
| May 21, 2010 at 15:57 | comment | added | Peter Arndt | This one is short and crisp: math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf | |
| May 21, 2010 at 15:45 | comment | added | Chris Schommer-Pries | I recommend: Brown, R. "Groupoids and van Kampen's theorem." Proc. London Math. Soc. (3) 17 1967 385--401. This is one of the earliest references. | |
| May 21, 2010 at 14:03 | comment | added | Andrea Ferretti | You can find it here: mathonline.andreaferretti.it/books/view/18/… | |
| May 21, 2010 at 12:56 | comment | added | Akela | Thanks! Very nice, once I figure it out fully. Could you also please provide a reference wherein such a Van-Kampen theorem for groupoids is considered | |
| May 21, 2010 at 12:31 | history | answered | Chris Schommer-Pries | CC BY-SA 2.5 |