12
$\begingroup$

I don't know anything about group cohomology and I'd like to.

What is the best text to learn this subject?

I'd prefer as soft an introduction as possible - that is, lots of motivation, lots of examples, slow moving development of intuition. (Something like Simmons' Intro to Category Theory, if you've read that.) I have a background in finite group theory and some character theory. The text should actually show how to compute group cohomologies, preferably not too far in, something I have not found in the group cohomology books in my University library.

A textbook would be great, but good lecture notes or papers would be fine too.

$\endgroup$
5
$\begingroup$

For many reasons, I would suggest Weibel's "Intro to Homological Algebra", because it puts things like "group cohomology" into a somewhat larger context, enabling comparisons to other things... Perhaps no reason to be a complete slave to the ordering of topics therein... but to see that "group cohomology" consists of the right-derived functors of the "fixed-vector" functor (and "group homology" of left-derived functors of "co-fixed-vector" functor), as an example comparable to Lie-algebra (co-) homology, and many others, makes it easier to understand each particular example.

$\endgroup$
  • $\begingroup$ Brown's "Cohomology of groups" is another standard reference. $\endgroup$ – Moishe Kohan Mar 4 '14 at 0:30
  • 1
    $\begingroup$ I would like to recommend Serre's "Local Fields" for finite groups, and "Galois Cohomology" for profinite groups. $\endgroup$ – nguyen quang do Mar 24 '16 at 21:23

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.