Timeline for Compelling evidence that two basepoints are better than one
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Aug 17, 2015 at 11:28 | comment | added | Ronnie Brown | @Ryan I just mention that looking at groupoids led me to higher homotopy Seifert-van Kampen Theorems and that led eventually to nonabelian tensor products of groups of which the bibiliography on my web page has 131 items, the majority by group theorists: see pages.bangor.ac.uk/~mas010/nonabtens.html. | |
| Jan 29, 2014 at 21:24 | comment | added | Ronnie Brown | @Ryan: "terminology preferences" can be very useful. An extreme example is Roman numerals versus Arabic numerals. I also tend to take the line expressed by the question: "Is there compelling evidence that that one can do better without one hand strapped behind ones back?" Or, as Gian-Carl Rota wrote on another matter: "Exterior algebra is not meant to prove old facts, it is meant to disclose a new world. Disclosing new worlds is as worthwhile a mathematical enterprise as proving old conjectures.” The idea of groupoids has led me to new worlds, and modes of expression. What fun! | |
| Oct 8, 2010 at 16:39 | comment | added | Aaron Mazel-Gee | Right. Okay. . | |
| Oct 8, 2010 at 16:38 | comment | added | Aaron Mazel-Gee | (or equivalently a map $M\rightarrow BG$?) | |
| Oct 8, 2010 at 16:27 | comment | added | Ryan Budney | That's very much my point and the point of the thread -- is usage of groupoids more than a terminology preference? | |
| Oct 8, 2010 at 16:20 | comment | added | Aaron Mazel-Gee | @ Ryan: Isn't a bundle of coefficient groups equivalent to a map $\pi_1(M,*) \rightarrow G$? If that's right, then you could refer to a bundle of groups without reference to the fundamental group, but it'd still be lurking in there somewhere. I.e., fundamental-groupy stuff is exactly the thing that makes local coefficients interesting. And, to bring it back to the original question, I'd imagine that this should induce a map (functor?) $\Pi_1(M) \rightarrow G$? | |
| Oct 4, 2010 at 15:27 | comment | added | Ryan Budney | I'm not following, either. Steenrod's local coefficient system formulation isn't the only formalism available. A lot of people think of a system of coefficients as a "bundle of groups". This avoids mentioning the fundamental group(oid) completely. | |
| Oct 4, 2010 at 13:02 | comment | added | Daniel Moskovich | I sort-of follow, but not quite. What, explicitly, are the choices when you say "with these choices"? | |
| Oct 4, 2010 at 11:56 | history | answered | Laurence Taylor | CC BY-SA 2.5 |