Timeline for Fundamental group as topological group
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Jun 2, 2010 at 7:51 | comment | added | David Roberts♦ | As I wrote the material on the nlab, I should point out that 'composition is no longer continuous' does refer to the quotient topology of the path space. And the stabiliser groups of this topologised fundamental groupoid are, under the stated conditions, discrete, because then the universal (connected) covering space is the source fibre at any point, and the fundamental group has then underlying space the fibre of the covering space at the basepoint chosen. | |
| Jun 1, 2010 at 11:08 | comment | added | Andrew Stacey | I just found what looks like a relevant paper on the arXiv and added the link to my answer. | |
| Jun 1, 2010 at 11:02 | comment | added | David Carchedi | Good point. I was wondering if this perhaps lines up with why "the plot thickens". | |
| Jun 1, 2010 at 10:35 | comment | added | Andrew Stacey | I'm embarrassed that I didn't spot the nlab link! However, note that: 1) there are conditions on the space which don't appear to be present in the paper in question; 2) the topology is not (always?) the same as that discussed in the paper in question (see the green box); 3) there is the statement "composition is no longer continuous" (and this may be using the quotient topology). | |
| Jun 1, 2010 at 10:20 | history | answered | David Carchedi | CC BY-SA 2.5 |