Timeline for Representation of Groupoids

Current License: CC BY-SA 4.0

6 events

when toggle format	what		by	license	comment
Jun 17, 2023 at 9:49	history	edited	Duchamp Gérard H. E.	CC BY-SA 4.0	groupes ---> groups
Apr 20, 2012 at 20:04	history	edited	AFK	CC BY-SA 3.0	added 6 characters in body
Sep 18, 2011 at 20:14	comment	added	Ronnie Brown		Just to say that YBL's apparent statement of the van Kampen theorem involves products and needs to be modified! I got into groupoids in the 1960s through being annoyed that the usual van Kampen theorem as formulated by Crowell could not compute the fundamental group of a basic exmple in topology, the unit circle! A meeting with George Mackey in 1967 at Swansea, where he told me of his work on ergodic theory using groupoids, and thus from an entirely different direction to mine, suggested there was more in this than met the eye. And Mackey's work directly influenced that of Connes.
Jun 26, 2011 at 5:40	comment	added	Alain Valette		On the other hand, the second proof of Yu's result (see Skandalis, G.; Tu, J. L.; Yu, G. The coarse Baum-Connes conjecture and groupoids. Topology 41 (2002), no. 4, 807–834) clearly separates the role of general locally compact groupoids, and of those associated with coarse metric spaces, and helps you get a clearer understanding of the situation.
Jun 26, 2011 at 5:37	comment	added	Alain Valette		I'm certainly not a fan of groupoids, but I agree with the statement that they can make statements and sometimes proofs much simpler. Consider for example G. Yu's result that finitely generated groups coarsely embedding into Hilbert space, satisfy the Novikov conjecture (see Guoliang Yu, The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space. Invent. Math. 139 (2000), no. 1, 201–240): the original proof is really technical and hard to grasp. (Continued in the next comment)
Feb 26, 2010 at 19:17	history	answered	AFK	CC BY-SA 2.5