Timeline for How do subgroups of fundamental groups relate to torsors
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 19, 2012 at 17:26 | vote | accept | Harry | ||
| Mar 19, 2012 at 6:38 | answer | added | Dan Petersen | timeline score: 6 | |
| Mar 18, 2012 at 21:11 | comment | added | Jason Starr | There is a mistake in your statement. The group $H^1(X,G)$ is in bijective correspondence with homomorphisms $\pi_1(X,x)\to G$ up to conjugacy. The kernel is a normal subgroup, but the quotient need not equal $G$ -- only a subgroup of $G$. | |
| Mar 18, 2012 at 19:31 | comment | added | HJRW | That should have been 'Arbitrary connected covers of degree $n$...' If you don't require connectedness, you can also drop the transitivity assumption. | |
| Mar 18, 2012 at 19:03 | comment | added | HJRW | I feel like you're looking for something like the following. Galois covers of a topological space $X$ of degree $n$ correspond to homomorphisms $\pi_1X\to S_n$ where the image is transitive and has trivial point stabilizers. Arbitrary covers of degree $n$ correspond to homomorphisms $\pi_1X\to S_n$ where the image is just transitive. No doubt this can be phrased in terms of something torsorish --- the answer should be approximately '$H^1(X,Y)$ where $Y$ is a transitive-but-not-necessarily-simply-transitive $G$-set'. | |
| Mar 18, 2012 at 17:15 | history | asked | Harry | CC BY-SA 3.0 |