Friday, April 8, 2011

??so consider ... "czech cohomology (of space x...) with coefficients in discrete non-abelian group g" ... ???...

???something about ... ??? 1-groupoid of g-torsors over x ... ???h^1(x,g) as set of iso classes of g-torsors over x, and h^0(x,g) as (non-abelian ...) aut gp of the trivial g-torsor over x ??? (??what _about_ aut gp of non-trivial torsor, and so forth ?? ... hmmm.... "twisted" ... ??...) ???is this correct??? ... ???try case x = k(g',1) ??? ... for example g' = z; then h^1 = conjugacy classes of g, and h^0 = ... ???maybe g???

(test some stuff here in part by thinking "simplicially"... and so forth ...???...)

??this as all depending only on "1-truncation" of x??? ...?? ...

??_is_ this all on the wrong track??? ...???...

??what about maybe ... ???some relatively minor level slip involving 1 vs 2 ... ???and so forth ... ??...


???then consider "stable" case, and so forth ... ??...

???something about ???homming "positive" spectrum into "neutral" one ... ????as giving "negative" one, or what??? ... and so forth ...


???something about ... ???recently asked about "what happens when globalization degenerates into cohomology theory", or something ... ?? but then also something about... taking seriously thinking of "globalization" as "like a cohomology theory" ... and so forth ... ???...

??what _about_ "obstruction" ??? ....

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