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Results tagged with at.algebraic-topology
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user 4231
Homotopy theory, homological algebra, algebraic treatments of manifolds.
3
votes
Accepted
Stabilizers for nilpotent adjoint orbits of semisimple groups
To supplement what Francois Ziegler says, I'd point out that the structure of semisimple complex Lie groups has been developed piecemeal over a century or so. The basic results on nilpotent elements …
- 12.9k
22
votes
Accepted
Cohomology of Flag Varieties
Borel's lengthy 1953 Annals paper is essentially his 1952 Paris thesis. It was
followed by work of Bott, Samelson, Kostant, and others, which eventually answers your
side question affirmatively. …
- 52.9k
3
votes
What's a good example/reference for cohomology classes on Springer fibers that aren't restri...
I think the standard early reference is the paper by Hotta and Springer here, in which they work with $\ell$-adic cohomology (but the results seem to carry over to other settings). What they show is …
- 52.9k
9
votes
Accepted
Proof for which primes H*G has torsion
I can't answer this completely, but I can point out some important follow-ups in the literature by Borel and others which need to be be taken into account. Borel's Tohoku paper is reprinted in the s …
- 52.9k
7
votes
connected compact semisimple lie group finite fundamental group
Besides Samelson's short 1946 research note linked by Mrc Plm, it's also useful to mention his longer 1952 survey on topology of Lie groups here (see Section 10 and references for various proofs of …
- 52.9k
11
votes
When are all centralizers in a Lie group connected?
I'm not sure whether the questions here concern just compact connected Lie groups, but in general the connectedness of centralizers involves some subtleties and may not be dealt with definitively in b …
- 52.9k
4
votes
Weight lattice and the fundamental group
Jesper Grodal's reference to Bourbaki is a reasonable one for these questions, including 1). There are also two volumes in the Springer GTM series which treat many aspects of compact Lie groups, inc …
- 52.9k
3
votes
Presentation of the pure Artin groups
The question is stated a bit loosely, but the basic literature goes back about four decades to work of Brieskorn and Deligne. Since I'm not an expert on these matters I can only refer to the basic …
- 52.9k
22
votes
Is there a Morse theory proof of the Bruhat decomposition?
It may be useful to expand Steven Sam's partial answer. This isn't really an answer to the original question, but is too long for a comment. The discussion in Chriss-Ginzburg 2.4, which relies on ma …
- 52.9k