Timeline for Residual finiteness: why do we care?

6 events

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Dec 29, 2017 at 8:59	comment	added	HJRW		Another important application would be to constructing families of expanders. Since we're good at constructing hyperbolic groups with property T, and Margulis proved that the Cayley graphs of the finite quotients of a property T group form a family of expanders, the residual finiteness of hyperbolic groups would imply the existence of large families of expanders.
Feb 28, 2015 at 9:16	comment	added	HJRW		But this is an example of a question becoming less important because approaches to it are successful, which surely is evidence for the importance of the original question, rather than against it.
Feb 28, 2015 at 9:05	history	edited	HJRW	CC BY-SA 3.0	Added one more application.
Feb 28, 2015 at 8:54	comment	added	HJRW		I'll add that, in response to the first question, I think we care less than we used to about whether or not all hyperbolic groups are residually finite. In practice, many of the examples we can build are not just hyperbolic but virtually special, and so have all the 'profinite' properties we might want.
S Feb 28, 2015 at 4:30	history	answered	HJRW	CC BY-SA 3.0
S Feb 28, 2015 at 4:30	history	made wiki			Post Made Community Wiki by HJRW