Timeline for For a cross section $\sigma\colon G/N\to G$, how is $\sigma(y)^{-1}\sigma(x)^{-1}\sigma(xy)$ called?

8 events

when toggle format	what		by	license	comment
Mar 5, 2015 at 9:18	vote	accept	Hannes Thiel
Mar 3, 2015 at 19:54	answer	added	Dave Witte Morris		timeline score: 6
Mar 3, 2015 at 10:18	comment	added	David Roberts♦		Your second sentence is correct. The issue with "the cocycle" is that there seem to be more than one sort of cohomology lying around, one for each definition of cocycle.
Mar 3, 2015 at 10:17	comment	added	Hannes Thiel		Ah I see. Thanks. But then what is "the cocycle" associated to the cross section? Maybe there are two. One measuring if the extension is split, and one measuring if the section is multiplicative.
Mar 3, 2015 at 10:10	comment	added	David Roberts♦		I disagree, the usual notion of 2-cocycle in $H^2(G/N,N)$ is a function $G/N\times G/N \to N$, measuring exactly how $N\to G \to G/N$ fails to be a trivial extension. This is different to measuring if the extension is a split extension or not.
Mar 3, 2015 at 10:08	comment	added	Hannes Thiel		Really? The usual cocycle for the section $\sigma$ is the map $\omega\colon G\times G/N\to N$, defined by the formula $\sigma(gy)\omega(g,y)=g\sigma(y)$. If $\sigma$ is multiplicative (which means that $G$ is a semidirect product), then $\alpha$ is trivial, but the cocycle $\omega$ need not be. How can this be?
Mar 3, 2015 at 10:01	comment	added	David Roberts♦		It is exactly a cocycle, in nonabelian cohomology of groups.
Mar 3, 2015 at 8:55	history	asked	Hannes Thiel	CC BY-SA 3.0