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Results tagged with at.algebraic-topology
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user 35575
Homotopy theory, homological algebra, algebraic treatments of manifolds.
15
votes
1
answer
6k
views
Exactness of 2nd-Order Differential Equations via Differential Forms
This (probably very elementary) question came up the last time I taught differential equations, and I've been toying with it for a while with no success:
A 1st-order differential equation $M(x,y)dx+N …
- 8,467
9
votes
Essential theorems in group (co)homology
Shapiro's lemma and dimension-shifting. Cohomology of cyclic groups and Herbrand quotients.
It would be helpful to know what you need to know group cohomology for.
If you have an interest in pr …
31
votes
3
answers
3k
views
Why aren't there more classifying spaces in number theory?
Much of modern algebraic number theory can be phrased in the framework of group cohomology. (Okay, this is a bit of a stretch -- much of the part of algebraic number theory that I'm interested in...) …
- 8,467
9
votes
Geometric interpretation of the lower central series for the fundamental group?
A special case you might find informative: If $L$ is a link in $S^3$, then Chen-Milnor theory gives you a presentation of the link group $\pi=\pi_1(S^3-L)$ modulo some deeper terms of the the lower c …
- 8,467